THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 

GIFT  OF 

John  S.Prell 


' 


MACHINE    DESIGN 


PART    I. 

FASTENINOS 


BY 

WILLIAM    LED  YARD    CATHCART 

ADJUNCT  PROFESSOR  OF  MECHANICAL  ENGINEERING,  COLUMBIA  UNIVERSITY;    MEMBER 
AMERICAN  SOCIETY  OP  MECHANICAL  ENGINEERS;  MEMBER  OP  THE  AMERICAN 
SOCIETY  OF  NAVAL  ENGINEERS;  MEMBER  OF  THE  SOCIETY  OF 
NAVAL  ARCHITECTS  AND  MARINE  ENGINEERS. 


NEW  YORK 

D.  VAN    NOSTRAND    COMPANY 

23  MURRAY  AND  27  WARREN  STS. 

1903 

JOHN  S.  PRELL 

Civil  &  Mechanical  Engineer. 

SAN  FRANCISCO,  CAL. 


COPYRIGHT,  1903,  BY 
D.   VAN  NOSTRAND  COMPANY 


Eagiwerug 
Library 

TJ 


Y.I 

PREFACE. 

THE  main  purpose  of  this  book  is  to  present,  in  compact  lorm 
for  the  use  of  the  student  and  designer,  modern  American  data 
from  the  best  practice  in  the  branch  of  Machine  Design  to  which 
the  work  refers.  The  theoretical  treatment  of  the  subject  has 
also  been  given  fully  ;  but  this  has  been  done  for  completeness 
only,  since  that  field  has  been  covered  exhaustively  by  able  writers- 
Scientific  analysis  and  the  records  of  practice  are  both  essential 
to  success  in  the  design  of  machine  members,  but  neither  alone  is 
trustworthy.  The  former  predicts  only  those  stresses  which  pre- 
vail under  normal  conditions  arid  ignores  the  overload,  the  rough 
handling,  or  the  slight  accident  which  the  machine  may  meet  and 
against  which  it  should  not  fail.  Practical  data,  on  the  other 
hand,  show  only  the  proportions  which  constructors  have  given 
in  specific  cases  of  stress  and  service  and  empirical  formulae 
founded  upon  them  may  give  results  wide  of  the  mark,  if  the 
inherent  limitations  of  these  formulae  be  exceeded.  The  problem 
of  design  is  one  whose  many  elements  vary  continually  in  num- 
ber, character,  and  magnitude,  and,  for  its  solution,  theoretical 
analysis,  precedent,  and  the  ripened  judgment  of  the  designer 
are  required. 

Elsewhere  acknowledgment  has  been  made  of  the  courtesy  of 
the  many  officials  and  companies  who  have  furnished  information. 

^  The  author's  thanks  are  due  especially  to  Rear  Admiral  George 
W.  Melville,  Engineer-in-Chief,  U.  S.  Navy  ;  Professor  Philip  R. 
Alger,  U.  S.  Navy  ;  Professor  J.  Irvin  Chaffee  ;  Leo  Morgan,  Esq.; 
J.  M.  Allen,  Esq.,  President  the  Hartford  Steam  Boiler  Inspection 
and  Insurance  Company  ;  C.  C.  Schneider,  Esq.,  Vice  President 
the  American  Bridge  Company  ;  Messrs.  William  Sellers  and 

a  Company  ;  the  Baldwin  Locomotive  Works  ;  and  the  Newport 
News  Shipbuilding  and  Dry  Dock  Company.  The  author  desires 

£3  also  to  express  his  deep  indebtedness  to  Stevenson  Taylor,  Esq., 

Ci    President  of  Webb's  Academy  and  Vice  President  of  the  W.  and 
A.  Fletcher  Co.,  whose  examination  of,  and  additions  to,  the  text 
have  added  materially  to  the  value  of  this  work. 
COLUMBIA  UNIVERSITY,  NEW  YORK, 


IO  February,  1903. 


733412 


CONTENTS. 


CHAPTER  I. 

PACK. 

SHRINKAGE  AND  PRESSURE  JOINTS  :......       i 

i.  General  formulae.  2.  Proportions  of  the  joint.  3.  Metals. 
4.  Forcing  pressures.  5.  Shrinkage  temperatures.  6.  Shrinkage 
vs.  pressure  fits.  7.  Stationary  engines,  data  from  practice.  8. 
Marine  engines,  data  from  practice.  9.  Railway  work,  data  from 
practice.  10.  Shrinkage  in  gun  construction. 


CHAPTER  II. 

SCREW  FASTENINGS  :  .         .         .         .         .         .         .         .42 

ii.  Triangular  vs.  square  threads.  12.  Requirements  of  the 
screw-thread.  13.  Elements  of  the  screw-thread.  14.  The  U.  S. 
standard  (Sellers)  thread.  15.  Modifications  of  the  Sellers  system. 
16.  The  sharp  V  thread.  17.  The  Whitworth  thread.  18.  The 
sharp  V,  Sellers,  and  Whitworth  threads.  19.  The  French  Stand- 
ard thread.  20.  The  International  Standard  thread.  21.  The 
British  Association  Standard  thread.  22.  The  square  thread.  23. 
The  |--V  thread.  24.  Special  threads.  25.  Machine  and  wood 
screws.  26.  Pipe  threads.  27.  Stresses  in  screw-bolts.  28. 
Stresses  in  nuts.  29.  Efficiency  of  the  screw.  30.  Types  of 
screw  fastenings.  31.  Methods  of  manufacture.  32.  Materials. 
33.  Nut -locks.  34.  Wrenche  s. 

CHAPTER  III. 

RIVETED  JOINTS  :  THEORY  AND  FORMULAE  :  .         .         .         .127 

35.  Rivets.  36.  Proportions  of  rivets.  37.  Rivet  and  plate 
metals.  38.  Rivet-holes.  39.  Boiler-seams :  longitudinal,  cir- 
cumferential, and  helical.  40.  Forms  of  riveted  joints.  41.  The 
elements  of  a  riveted  joint.  42.  The  theoretical  strength  of  riveted 
joints.  43.  General  formulae  for  boiler-joints.  44.  The  thickness 
of  shell  sheets.  45.  The  stresses  in  riveted  joints.  46.  The  fric- 
tion of  riveted  joints. 

v 


vi  CONTENTS. 

CHAPTER  IV. 

RIVETED  JOINTS  :  TESTS  AND  DATA  FROM  PRACTICE  :      .         .         .192 

47.  Tests  of  multiple-riveted,  double-strapped  butt  joints.  48. 
Riveting  machines.  49.  Riveted  joints,  marine  boilers.  50.  Riv- 
eted joints,  locomotive  boilers.  51.  Riveted  joints,  stationary 
boilers.  52.  Riveted  joints,  structural  work.  53.  Riveted  joints, 
hull  plating. 

CHAPTER  V. 

KEYED  JOINTS:    PIN-JOINTS:       . 251 

54.  Forms  of  keys.  55.  Proportions  of  keys.  56.  Stresses  on 
keys.  57.  Through-keys:  forms.  58.  Through-keys:  stresses. 
59.  Pin-joints. 


TABLES. 


I.  Shrinkage  vs.  Pressure  Fits  (Wilmore)        .         .         -          .      15 
II.   Pressure  Fits  (Lane  and  Bodley  Co.)      B'..         .         .          .      17 

III.  Shrinkage  and  Pressure  Fits  (Russell  Engine  Co.)       .  17 

IV.  Pressure  Fits,  Stationary  Engines        .         .          .         .         .18 
V.  Shrinkage  and  Pressure  Fits  (Buffalo  Forge  Co.)         .         .18 

VI.  "  "          "          "     (B.  F.  Sturtevant  Co.)    .         .     18 

VII.  "  "  "  "     Summary  of  Practice      .         .      19 

VIII.  "  "  "  "     (Union  Iron  Works)        .         .     23 

IX.  "         Fits  (Am.   Railway  Master  Mechanics'    Asso'n)     25 

X.  U.  S.  Standard  (Sellers)  Bolts  and  Nuts      .         .          .          .50 

XL  Standard   Bolts   and  Nuts,   U.  S.   Navy  (Bureau  of  Steam 

Engineering)  .          .          .          .          .          .          .  52 

XII.   Manufacturers'   Standard    Dimensions  of  Bolt-heads  (Am. 

Iron  and  Steel  M'f  g  Co.) 53 

XIII.  Manufacturers'   Standard  Dimensions  of  Hot-pressed  Nuts 

(Am.  Iron  and  Steel  M'f'g  Co.)       .          .          .          .          -53 

XIV.  Round  Slotted  Nuts  (Newport  News  Shipbuilding  and  Dry 

Dock  Co.) 54 

XV.  Whitworth  System,  Bolts  and  Nuts 55 

XVI.   French  Standard  Screw  Threads 58 

XVII.   International  Standard  Screw  Threads        .         .         .         -59 

XVIII.   British  Association  Standard  Thread 60 

XIX.  Standard  Square  Threads  (William  Sellers  and  Co.)   .         .     61 
XX.  Standard   Square  Threads   (Newport  News  S.  B.  and   D. 

D.  Co.) .62 

XXI.   X-v  Screw  Thread  (William  Sellers  &  Co.)         ...     63 
XXII.   Standard  Bastard  Screw  Threads  (Newport  News  S.  B.  & 

D.  D.  Co.) 64 

XXIII.  Acme  Standard  (29°)  Screw  Thread 65 

XXIV.  Proportions  of  Armor  Bolts,  U.  S.  Navy     .         .         .         .66 
XXV.   Machine  Screws  (Tyler) 69 

XXVI.  Wrought  Iron  Welded  Tubes  (Briggs'  Standard)         .         .71 
XXVII.  Ratio     of    Bearing    Pressure    to    Tensile    Stress    (Sellers 

Threads)        .........     74. 

XXVIII.    "  Grooved  "  Specimens  (Howard) 76 

XXIX.  Threaded  and  "  Grooved  "  Specimens  (Martens)         .         .     77 
XXX.  Coefficients  of  Friction  for  Square  Threads  (Kingsbury)    .     88 
Coefficients  of   Friction  With  Various  Lubricants   (Kings- 
bury)    .        ,         .         .  .         .         .         .         .88 

vii 


viii  TABLES. 

XXXI.   Steel  Studs  for  Cylinder  Covers  (U.  S.  Navy)      ...     94 
XXXII.  Approximate  Efficiencies  of  Square  Threaded  Screws  (Good- 
man)       ..........     97 

XXXIII.  Safe  Loads  for  U.  S.  Standard  Bolts  (Williams)  .          .          .103 

XXXIV.  Tap-bolts  and  Set-screws  (Newport  News  S.  B.  and  D.  D. 

Co.) 105 

XXXV.   Eye-bolts  (Union  Iron  Works) 107 

Dimensions    and   Conditions    of  Stay-Bolts    (Sprague   and 

Tower) 108 

XXXVI.  Collar  Nuts  with  Locking  Screws  (Union  Iron  Works).          .    121 

XXXVII.   Engineers'  Wrenches,  Single  Head  (J.  H.  Williams  &  Co.)   124 

XXXVIII.  Check-Nut  Wrenches  (J.  H.  Williams  &  Co.)      .         .         .125 

Wrenches,  International  Standard  Nuts      .         .         .         .126 

XXXIX.   Proportions  of  Rivet-Heads  (Am.  Iron  and  Steel  M'f  g  Co.)   128 

XL.   Proportions  of  Rivet-Heads  (Champion  Rivet  Co.)       .          .129 

Tests  of  Drilled  and  Punched  Plates  (Kirkaldy)  .          .          .137 

Efficiencies  of  Butt  Joints,  Double-Strapped  (Traill)    .          .163 

XLI.  Tests  of  Multiple  Riveted,  Double-Strapped,  Butt-joints  (U. 

S.  Navy)        . 196 

XLII.   Boiler  Rivets  (U.  S.  Navy)         ...         .         .         .207 

Proportions  of  Joints,  Cylindrical  Boilers  (U.  S.  Navy)         .   208 
Weight  of  Boiler  Rivets  (U.  S.  Navy)         .         .         .         .209 

XLIII.   Locomotive   Boilers,     Single   Riveted   Longitudinal   Seams 

(Baldwin  Locomotive  Works).         .         .         .         .         .211 

XLIV.   Locomotive  Boilers,  Double  Riveted  Seams  (Baldwin  Loco- 
motive Works) 212 

XLV.   Locomotive  Boilers,  Quadruple  Butt-joint  Seams  with  Welded 

Ends  (Baldwin  Locomotive  Works).          .         .         .         .212 
XLVI.   Sextuple  Butt-joint  Seams  with  Welded  Ends  (Baldwin  Loco- 
motive Works)       .         .          .213 

Locomotive  Boilers,    Location   and    Proportions    of  Seams 
(Baldwin  Locomotive  Works).          .          .          .          .          .214 

XLVH.,  XLVIII.,  XLIX.,  L.     Stationary  Boilers,  Riveted  Joints  (Hart- 
ford Steam  Boiler  Inspection  and  Insurance  Co.).         218,  219 
LI.   Proportions  of  Rivet-Heads  (American  Bridge  Co.)      .          .   220 

Weight  of  Rivets,  Structural  Work 221 

LII.   Staggering  of  Rivets  (American  Bridge  Co.)         .          .          .   222 

LIII.   Rivet  Spacing  in  Angles  (Am.  Bridge  Co.)  .         .          .   223 

LIV.   Shearing  and  Bearing  Values  of  Rivets  (Am.  Bridge  Co.)    .   225 

LV.   Angles,  Sectional  Area  (Am.  Bridge  Co.)    .     '    .         .          .230 

LVL,  LVII.  Riveted  vs.  Bolted  Joints  (Berlin  Iron  Bridge  Co.)       .   234 

LVII-A,  LVIII.   Proportions  of  Seams  and  Rivets,   Torpedo-boat  and 

Ship-work  (U.  S.  N.)      .....   240,  241 

LIX.   Diameter  of  Rivers,  Hull-work  (U.  S.  N.)  .          .          .          .   242 

LX.   Allowance  for  Rivet-Points,  Hull-work  (U.  S.  N.)         .          .   243 


TABLES.  ix 

LXI.  Breadth  of  Laps  and  Straps,  Hull-work  (U.  S.  N.)  .  .  243 
LXII.  Spacing  of  Rivets,  Hull-work  (U.  S.  N.)  .  .  .  .244 
LXIII.  Minimum  Thickness  of  Outside  Plating  and  Flat  Plate  Keel 

(American  Bureau  of  Shipping) 246 

LXIV.   Diameter  of  Rivets,  Breadth  of  Laps,  Lapped  Butts,  Width 
of  Butt-straps,  and  Breadth  of  Edge  Strips  on  Plate  Seams, 
Hull-work  (American  Bureau  of  Shipping)         .          .          .   247 
Plating  and  Transverse  Seams  (Am.  Bu.  Shipping)  .          .   250 
LXV.   Square  Keys  (Richards)     .          .          .          .          .          .          .257 

LXVI.   Flat  "  " 257 

LXVII.   Feather     "  " 257 

LXVIII.    Keys  for  Shafting  (William  Sellers  and  Co.)         .          .          .258 

LXIX.  "      Machine  Tools  (William  Sellers  and  Co.)        .          .    258 

LXX.   Key-ways  for  Milling  Cutters  (Brown  and  Sharpe  M'f'g  Co.)  259 

LXXI.   Stationary  Engines,  Crank  and  Wheel  Keys        .          .          -259 

LXXII.   Marine  Engines,  Keys  and  Key-ways  (Newport  News  S.  B. 

and  D.  D.  Co.) 260 

Taper-Pins  (Morse  Twist  Drill  and  Machine  Co.)          .          .   268 

LXXIII.   Stationary  Engines,  Connecting  Rod  Ends,  Bolted  Strap      .    269 

LXXIV.   Maximum  Bending  Moments  on  Pins  (American  Bridge  Co.)  280 

LXXV.    Pins  with  Lomas  Nuts  (Am.  Bridge  Co.)      ....    282 

LXXVI.          "         Cotters  "  ""....   283 

LXXVII.  Eye-Bars  (Am.  Bridge  Co.) 284 


AUTHORITIES   QUOTED. 


Alger,  Prof.  Philip  R.,  U.  S.  N.,  29 
Allen,  J.  M.,  134,  192 
American  Boiler  Manufacturers'  Asso- 
ciation, 215 
"        Bridge  Company,  219,  220, 


222,   223,   225, 
to  284,  inc. 


230,  280 


Bureau  of  Shipping,  245  to 

250,  inc. 

"        Engineer  and  Railroad  Jour- 
nal, 134,  266 
Iron  and  Steel  M'fg  Co., 

53,  78,  128 

Machinist,  104,  105,  203 
"        Railway  Master  Mechanics' 
Asso'n,  25 

Bach,   Prof.  C.,   181,    187,   188,  189, 

191 
Bailey,  F.  H.,  Lieut.  Com'd'r,  U.  S. 

N.,  261 
Baldwin  Locomotive  Works,  192,  210 

to  214,  inc. 

Barr,  Prof.  John  H.,  100 
Bauschinger,  Prof.,  133 
Berlin  Iron  Bridge  Co.,  234,  235 
Birnie,   Major  Rogers,  U.  S.  A.,  28, 

29 

Bond,  Geo.  M.,  50,  68 
Box,  Thos.,  78 
Briggs,  Robert,  69,  70 
Broomall,  14 
Brown    and  Sharpe  M'fg  Co.,   258, 

259 

Bryan,  C.  W.,  C.E.,  227,  233 
Buffalo  Forge  Co.,  16,  18 
Bulletin  Soc.  d'Encour,  59 
Bureau  of  Construction  and    Repair, 


Burr 


20,    51,    73,   94,    114, 
196,  205,  207,  277 
Prof.  W.  H.,  4,  13,  227 


134. 


U.  S.  N.,  66,  109,  237  to  244,  inc. 
Bureau  of  Ordnance,  U.  S.  N.,  66,  67    McBride,  Jas.,  99 
"    Steam  Engineering,  U.  S.   N.,  i  Meier,  E.  D.,  215 
x 


Canaga,  Com'd'r  A.    B.,   U.   S.   N., 

148 

Champion  Rivet  Co.,  129,  132 
Chief  of  Ordnance,  U.  S.  A.,  36,  67, 

192 
Cramp,  Edwin  S.,  236 

Wm.  S.  and  E.  B.  Co.,  192 
Clavarino,  6 
Colby,  A.  L.,  131 
Cotterill,  Prof.  J.  H.,  4,  277 

Goodman,  Prof.  John,  97 

Harlan  and  Hollingsworth  Co.,  24 
Hartford  Steam  Boiler  Insp.  and  Ins. 

Co.,  216  to  219,  inc.,  275 
Howard,  Jas.  E.,  75 

Johnson,  Prof.  J.  B.,  76,  133,  227 
Jones,  Prof.  F.  R.,  255 

Kennedy,  Prof.,  165 
King,  Major  W.  R.,  U.  S.  A.,  78 
Kingsburg,  Prof.  Albert,  87,  88 
Kirkaldy,  75,  78,  137 

Lame,  6 

Lane  and  Bodley  Co. ,  17 
Lanza,  Prof.  G.,  101,  105,  106 
Lewis,  Wilfred,  89,  98 
Lineham,  Prof.  W.  J.,  14 
Linnard,   Naval    Constructor  J.    H., 
U.  S.  N.,  236 

Marks,  W.  D.,  C.E.,  264 
Martens,  Prof.  A.,  76,  79,  91 


AUTHORITIES   QUOTED. 


Melville,  Rear  Admiral  Geo.  W.,  U. 

S.  N.,  112 

Merriman,  Prof.  M.,  6,  79 
Midvale  Steel  Co.,  22 
Morse  Twist  Drill  and  Machine  Co., 

268 

New  York  Shipbuilding  Co. ,  24 
Newport  News  Shipbuilding  and  Dry 

Dock  Co.,  54,  62,  64,  105,  260 
Niles  Tool  Works  Co.,  25 

Porter,  H.  F.  J.,  19 

Rankine,  Prof.  W.  J.  M.,  4,  182 
Reuleaux,   Prof.   F. ,   6,    13,   74,    166, 

168,  254 

Richards,  John,  257,  263 
Rivet-Dock  Co.,  113 
Russell  Engine  Co.,  17 
Schell,  Lieut.  Com'd'r,  U.  S.  N.,  171 
Seaton,  A.  E. ,  170 
Seaton  &  Rounthwaite,  102 
Sellers,  William,  &  Co.,   61,  63,  2-58 
Smith,  Prof.  A.  W.,  82 


Sprague,  Chief  Eng'r  Jas.  W.,  U.  S. 

N.,  108,  277 

Sternbergh,  J.  H.,  114,  128 
Stoney,  B.  B.,  127,  130,  165,  181 
Stromeyer,  C.  E.,  186 
Sturtevant,  B.  F.,  Co.,  17,  1 8 
Sweet,  Prof.  J.  E.,  82 

Thurston,  Prof.  R.  H.,  14 

Thury,  Prof.,  59 

Tower,  Chief  Eng'r  Geo.  E.,  U.  S.  N., 

108,  277 

Townsend,  David,  112,  136 
Traill,  Thos.  W.,  F.   E.   R.  N.,  134, 

163,    170,    171,    210 

Union  Iron  Works,  23,  107,  121 
Unwin,  Prof.  W.  C.,  86,  145,  185 
U.  S.  Board  of  Supervising  Inspectors 
of  Steam  Vessels,  209 

Weisbach,   Dr.  Julius,   74,    118,    119 
Whitney  M'f  g  Co.,  253 
Williams,  H.  D.,  101,  102 
Williams,  J.  H.,  &  Co.,  124,  125 
Wilmore,  Prof.,  150 
Wood,  R.  D.,  &  Co.,  202 


JOHN  S.  PRELL 

Civil  &  Mechanical  Engineer. 

SAN  FRANCISCO,  CAL. 

MACHINE  DESIGN. 


CHAPTER  I. 

SHRINKAGE  AND  PRESSURE  JOINTS. 

Rigid  connections  of  this  character  between  members  of  a  ma- 
chine or  structure  are  of  frequent  application.  The  inner  member 
of  the  pair  to  be  united  is  made  cylindrical  or  slightly  conical  in 
form  ;  the  corresponding  portion  of  the  outer  member  is  bored  so 
that  it  is  of  the  same  shape,  but  less  in  diameter  throughout. 
When,  therefore,  the  latter  is  made  to  encircle  the  former,  the  re- 
sulting radial  pressure,  acting  at  the  contact-surfaces,  produces  a 
frictional  resistance  to  relative  motion  of  the  parts.  In  a  Shrinkage 
Fit  or  joint,  the  outer  member  is  expanded  by  heating,  slipped  in 
place,  and  held  therein  by  the  subsequent  contraction  in  cooling.  In 
a  Pressure  ("Press"  or  "Forced")  Fit,  the  parts  are  driven  together 
by  hydraulic  pressure.  Joints  of  the  latter  type  are,  as  a  rule, 
restricted  to  members  of  moderate  size  —  crank-pins,  cranks,  and 
the  wheels  and  axles  of  engines  and  cars  being  familiar  examples. 
The  shrinkage  fit  is  applied,  not  only  in  the  union  of  large  mem- 
bers in  which  maximum  resistance  to  relative  motion  is  desired, 
as  in  the  crank-shafts  of  engines  of  high  power ;  but,  as  well, 
in  modern  ordnance,  where  results  of  extreme  accuracy  are  es- 
sential in  order  to  obtain  the  desired  inward  pressure  required  to 
withstand  the  outward  force  of  the  gases  generated  in  the  powder- 
chamber. 

i.    General  Formulae. 

The  final  diameter  of  a  joint  made  by  shrinkage  or  pressure  is 
intermediate  between  those  of  the  parts  before  union,  i.  e.,  the 
inner  member  has  been  compressed  and  the  outer  expanded. 
These  changes  and  the  elasticity  of  the  metal  produce  a  radial 
compressive  stress  acting  upon  both  members  at  the  contact-sur- 
faces and  a  consequent  circumferential  stress  or  "  hoop-tension  " 


MACHINE    DESIGN. 


fyS 


SHRINKAGE   AND    PRESSURE   JOINTS.  3 

within  the  outer  member.     The  latter  stress  is  a  maximum  at  the 
joint  and  decreases  rapidly  toward  the  exterior. 

i.  THIN  BANDS. — When  the  outer  member  is  thin,  as  a  band  or 
tire,  and  the  inner  is,  relatively,  of  large  diameter,  the  compres- 
sion of  the  latter  is  so  small  as,  frequently,  to  be  negligible  in 
practice.  The  stress  of  the  shrinkage  or  forcing  may  then  be 
considered  as  expended  wholly  in  the  expansion  of  the  band. 
Assume  then,  as  in  Fig.  I,  an  incompressible  hub  upon  which  is 
shrunk  such  a  band,  the  stress  upon  the  latter  being  within  the 
elastic  limit. 
Let: 

R0  =  original  radius  of  interior  of  band  ; 
R  =  radius  of  hub  ; 
t  =  tensile  unit  stress  within  band  ; 
et  =  unit  elongation  due  to  t ; 

E  =  modulus  of  elasticity  of  band-metal  =  —  ; 

/  =  unit  radial  pressure  ; 
b  =  breadth  (axial)  of  band  ; 
T=  thickness  (radial)  of  band,  expanded  ; 
/=  coefficient  of  friction. 
Then: 

Increase  in  length,  interior  of  band  =  2r:(R  —  R^) ; 
Original  length,  interior  of  band  =  27rR() ; 

r>  7p 

Elongation  per  unit  of  length  =  et  =  — ~ — ° ; 

-"-o 

/?  —   /? 

Unit  tensile  stress  =  t  =  Eet  =  E ^ — -.  (l) 

-^•o 

This  tensile  stress,  t,  acts  throughout  the  band,  tending  to  re- 
sist rupture  of  the  latter  on  any  diametral  plane,  as  A-B.  The 
total  resistance  opposed  thus  at  A  and  B  = 

2(6  x  Tx  t).  (2) 

The  unit  radial  pressure,  /,  acts  outward,  equally  at  all  points 
upon  the  band.  The  latter  is,  therefore,  virtually  in  the  condition 
of  a  thin  cylinder,  of  length  b  and  thickness  T,  subjected  to  in- 
ternal fluid  pressure.  In  Fig.  I  the  vertical  component  of  the 
pressure  /  is  that  which  tends  to  part  the  band  on  the  horizontal 


4  MACHINE   DESIGN. 

plane  A-B.  For  an  elementary  strip  of  the  band,  of  length  Rdd, 
and  of  breadth  b,  we  have  : 

Radial  force  on  elementary  strip  =  Rdd  x  b  x  p ; 
Parting  force,  elementary,  on  plane,  A-B  =  Rdd  x  b  x  /  sin  6; 

Parting  force,  total,  on  band  =  bpR  I   sin  6dd  =  2bpR.  (3) 

Equating  (2)  and  (3)  : 

Tt  (R-R^T 

P~  R-  RR0 

The  resistance  to  movement  at  the  contact-surface  is  equal  to  the 
product  of  the  area  of  that  surface,  the  radial  pressure,  and  the 
coefficient  of  friction,  /.  e.  : 

r>  rj 

Resistance  to  slip  =  E -= — -  •  2~bTf.  (5) 

2.  THICK  CYLINDERS. — The  method,  as  above,  disregards  the 
compression  of  the  inner  member,  assumes  the  stress  of  forcing 
or  shrinkage  as  expended  wholly  in  expanding  the  band,  and  con- 
siders the  unit-stress  within  the  latter  as  uniform  throughout  the 
cross-section.  The  inner  member  cannot  be  incompressible  and, 
therefore,  the  circumferential  stress  given  by  (i)  is  greater  than 
that  which  would  exist.  The  method  is  hence  applicable  only 
within  the  limits  noted.  In  an  outer  member  whose  walls  are  rel- 
atively thick,  the  stresses  at  various  radial  distances  differ  widely 
in  intensity  ;  and,  for  the  determination  of  their  magnitude,  recourse 
must  be  had  to  the  complex  formulae  deduced  for  the  investigation 
of  thick,  hollow  cylinders,  subjected  to  internal  fluid  pressure.  Of 
such  formulae,  those  founded  on  the  method  of  Lame  *  give,  with- 
out the  assumptions  of  Barlow  or  Brix,  the  character  and  intensity 
of  the  various  stresses  at  any  point  within  the  cylinder  walls. 

Thus,  consider,  as  in  Figs.  2  and  3,  a  horizontal  hollow  cylin- 
der, open  at  the  ends,  the  latter  being  faced  off  in  a  plane  normal 
the  axis.  Let  this  cylinder  be  filled  with  fluid,  which  is  forced 
inward  by  two  expanding  plungers  A,  A,  the  result  being  the 
production  of  a  fluid  pressure  upon  the  internal  surface  of  the 
wall.  From  the  construction  and  operation  it  is  clear  that,  as  the 
ends  are  free,  the  cylinder  will  remain  a  cylinder  under  stress ; 

*Rankine,  "Applied  Mechanics,"  1869,  p.  290.  Burr,  "  Elasticity  and  Resist- 
ance," etc.,  1897,  p.  36.  Cotterill,  "  Applied  Mechanics,"  1895,  p.  408. 


SHRINKAGE   AND    PRESSURE  JOINTS.  5 

that  a  transverse  section,  taken  normal  to  the  axis  "when  at  rest, 
remains  thus  normal  under  stress  ;  and  that,  on  such  a  section, 
the  resultant  longitudinal  stress  is  zero,  both  over  the  whole  area 
and  at  every  point  thereof.  Assume  that  the  material  is  isotropic 
and  that  no  stress,  at  any  point,  exceeds  the  elastic  limit. 
Consider  any  point  O  within  the  cylinder  wall.  Let : 

Ry  and  Rl  =  inner  and  outer  radii  of  cylinder  ; 

P0  and  Pl  =  inner  and  outer  pressures  upon  cylinder ; 

t  =  circumferential  stress  at  point  0  ; 
p  =  radial  pressure  at  point  0  ; 

/  =  longitudinal  stress  =  zero  at  point  O ; 

r  =  radius  of  point  0. 
Then,  from  the  deduction  in  §  10: 


(23) 


. 
R?  -  R*  R?  -  R*      '  r* 


f~~    <X°-*>'  +     °K?-V 


It  will  be  observed  that  the  circumferential  stress  /  varies  in- 
versely as  r2  and  is  therefore  a  maximum  at  the  cylinder-bore. 
This  condition  prescribes  the  useful  limit  of  thickness  for  cylinders 
which  are  not  under  exterior  compression.  No  such  cylinder  can 
be  made  sufficiently  thick  to  withstand  an  internal  pressure  per 
sq.  in.  greater  than  the  ultimate  tensile  strength  per  sq.  in.  of  the 
metal,  as  is  shown  by  equation  (19).  Since  the  working  pressure 
of  modern  ordnance  exceeds  considerably  the  elastic  limit  in  ten- 
sion of  the  material  used,  the  necessity  for  the  "  built-up  "  system 
is  apparent.  With  regard  to  formulae  (23),  it  will  be  observed 
also  that  t  may  be  either  tensile  or  compressive,  as  the  relations 
of  the  radii  and  pressures  determine ;  that  /  is  always  compres- 
sive ;  and  that  both  p  and  t  are  "  apparent "  and  not  "  true " 
stresses,  since  the  factor  of  lateral  contraction  has  not  been  intro- 
duced with  respect  to  them.  Considering  this  factor : 

True  Circumferential  Stress  =  /_J/_(_  J^).  (6) 

In  a  gun,  the  layer  in  which  the  breech-plug  houses  is  under  a  di- 
rect longitudinal  stress  /,  arising  from  the  pressure  upon  the  plug. 
This  stress  is  a  maximum  at  the  face  of  the  plug  and  diminishes 
rapidly  toward  the  muzzle.  If  the  apparent  values  of  /,  /  and  / 


6  MACHINE   DESIGN. 

be  substituted  in  (6),  the  working  equation  for  true  circumferential 
stress  will  be  obtained,  which  equation  is  Clavarino's  principal 
formula  for  the  investigation  and  design  of  guns.* 

3.  THICK  HUBS. — Professor  Reuleaux,  in  The  Constructor,^  gives, 
largely  without  deduction,  certain  working  formulas,  based  upon 
those  of  Lame  as  above,  which  are  especially  applicable  to  the 
shrinkage  or  cold  forcing  of  large  machine  members,  such  as 
cranks  and  wheel-hubs.  Thus,  consider  Fig.  4,  which  represents  a 
shaft  or  pin  A,  forced  into  a  ring  or  hub  B.  The  deduction  applies, 
theoretically,  to  either  shrinkage  or  forcing.  The  notation  is : 

Sv  =  radial  compressive  stress  at  r ; 

S2  =  circumferential  tensile  stress  at  r ; 

p  =  unit  radial  pressure  upon  contact-surfaces  =  Sl ; 
E^  =  modulus  of  elasticity,  inner  member ; 
E2  =  modulus  of  elasticity,  outer  member  ; 

r^  =  radius  of  pin  before  forcing ; 

r2  =  radius  of  hole  before  forcing ; 

r  =  radius  of  fit ; 

/   =  length  of  fit ; 

d  =  thickness,  outer  member,  after  forcing ; 

3        ,  _ri~r2          _Si 
r  '  rz  ^2' 

Q  =  maximum  forcing  pressure  required ; 
f  =  coefficient  of  friction  =  0.2. 

Under  the  conditions  shown  in  Fig.  4,  the  notation  of  equation  (23) 
giving  the  value  of  t,  when  translated  into  that  of  The  Constructor 
should  be  changed  thus  : 

ttoS2',  P0  to  5, ;  Pl  to  zero  ;  7?n  to  r ;  R^  to  r  -f  o  ;  r  remains  as  r. 
(a)  Stresses  and  Allowances. — Transforming  the  equation  for  t, 
in  accordance  with  the  above  : 


(7) 


*Merriman,  "  Mechanics  of  Materials,"  1899,  p.  318. 
f  Suplee's  Translation,  1895,  pp.  17,  18,  45-47. 


SHRINKAGE   AND    PRESSURE  JOINTS. 

In  Fig.  4 : 

Unit  deformation  (strain},  inner  member  =  — 


r  —  r. 


Unit  deformation  (strain),  outer  member  =  —  ; — -. 
From  the  definition  of  the  modulus  of  elasticity  : 

S,      r.-r  Sz      r  —  rz 

p  = and     T=r  = -.  (9) 

Adding  : 

rS±  +  r^  =  r-r  (10) 

Whence : 

By  definition  and  from  (10)  : 
From  (n)  and  (12) : 


vSj  and  vS2  are  mutually  dependent,  their  relation  being  expressed 
by  (7)  and  (8).     In  view  of  this  and  by  definition  : 

Si-Sf.  (64,O 

From  (36,  C~)  and  (64,  £")  : 

s,     SL    s     s* 


The  second  term  of  each  denominator  is  so  small  as  to  be  negli- 
gible.    Hence  : 


*  For  convenience  of  reference,  numbered  formulae  from  The    Constructor  are  given 
the  same  numeral,  with  "  C"  added. 


»  MACHINE   DESIGN. 

If  the  value  of  the  ratio  -,  be  assumed  or  known,  it  may  be  sub- 

stituted in  (7),  thus  giving  that  of  the  ratio,  -„-  =  p,  i.  e.  : 

If: 

d 

—  =  0.500,  i.ooo,  1.500,  2.000,  3.000  ; 

then 

p  =  0.385,  0.600,  0.724,  0.800,  0.882. 

Since  Ev  £2  and  the  allowable  value  of  S2  are  known  quantities, 
the  values  of  <p  and  Sl  may  be  found  from  (38,  C)  by  substitut- 
ing the  value  of  p. 

(b]  Forcing  Pressure.  —  The  force  necessary  to  press  a  cylindrical 
pin  into  a  hole  by  continuous  motion  may  be  taken  as  nearly  pro- 
portional to  the  rate  of  progress,  since  that  force  must  overcome 
a  resistance  which  is  largely  due  to  sliding  friction,  and  the  latter 
depends  upon  the  unit  pressure  on,  and  the  area  of,  the  surfaces 
in  contact.  The  force  will  be  a  maximum  just  as  the  pin  reaches 
the  end  of  the  hole.  From  Fig.  4  we  have  : 

Maximum  Forcing  Pressure  =  Q  =  2xr  x  /  X  Sl  x  f.      (62,  C) 
Radial  Pressure  =  S^=p  =  rfr.  (63,  C) 


(c)  Resistance  to  Slip,  either  axial  or  rotary,  is  given  by  the  value 
of  Q  in  (62,  C). 

(d}  The  Thickness  of  Hub  required  to  withstand  the  bursting 
pressure  corresponding  with  the  slip  resistance  Q,  as  above,  may 
be  found  by  combining  (62,  64,  C}.  Thus  : 

Q^27irlfS2x  p,  (13) 

in  which  Q  is  given  in  terms  of  the  circumferential  stress  at  the 
contact-surface.     From  (7),  (13)  and  (64,  C)  : 


whence  /         8\2       2iirlfS2  +  Q 


SHRINKAGE   AND    PRESSURE  JOINTS. 


and  Thickness  _8  _     \2xrlf S2  +  Q 

Radius    ~r~  \2zrt/St  -Q~1' 

from  which  the  required  thickness  d  may  be  found. 

(e)  Slip-resistance  vs.  Rotating  Force. — In  (66,  C)  Q  is  the  resist- 
ance opposed  by  the  fit  to  slipping  at  the  contact-surfaces;  its 
leverage  at  the  latter  is  r.  Assuming  the  hub  to  be  a  part  of  a 
wheel  or  crank  of  effective  radius  R,  and  the  external,  rotating  force 
at  that  radius  to  be  P,  we  have,  as  the  moment  of  the  latter  P  x  R, 
.-.Qxr^PxR.  (14) 

(/)  Coefficients  of  Friction  in  Forcing  and  Slip. — Assuming  that 
the  resistance  is  wholly  frictional,  it  is  apparent  that,  for  continu- 
ous forcing,  the  coefficient  of  friction  for  motion  should  be  used. 
Slipping  of  the  hub,  however,  must  occur  always  from  a  state  of 
relative  rest  of  the  members.  Therefore  in  (13)  and  (66,  C\  the 
coefficient  for  rest  applies.  With  the  high  radial  pressures  which 
prevail,  there  is  a  marked  difference  between  the  two  coefficients. 

2.    Proportions  of  the  Joint. 

Economy  of  material  prescribes  that  S0  shall  be  the  maximum  per- 
missible tensile  stress.  For  any  given  fit,  S2,  £}  and  £2  are  therefore 
constants,  while  the  radius  r  is  fixed  by  other  considerations  and  the 
length  /  is  known  approximately  or  accurately.  The  total  grip  Q 
required  would  determine  by  (66,  C)  the  value  of  the  thickness  d, 
if  the  coefficient  /  were  known  ;  but  experiments  indicate  that  the 
value  of  this  coefficient,  as  given  ordinarily  for  the  friction  of  motion 
between  the  clean  metallic  surfaces  considered,  is  not  a  safe  measure 
of  the  resistance  of  shrinkage  and  pressure  fits,  the  latter  especially. 
Such  investigation,  however/with  regard  to  the  value  of  f'm  these 
fits,  has  been  limited.  In  determining  d,  therefore,  there  should  be 
used,  preferably,  formulae  which  do  not  include  this  coefficient. 

From  (38,  C]  we  have: 

Total  allowance  /  i        p  \ 

Diameter       **  S*\E^  EJ  (I5) 

In  the  right-hand  member  all  quantities  are  known  except  p. 
From  (7)  and  (64,  C)  it  will  be  seen  that,  with  increased  thick- 
ness, f)  becomes  larger.  Therefore,  if,  with  the  same  diameter 
and  metals,  the  hub  be  made  thicker,  the  total  allowance,  the 
radial  pressure,  and  the  grip  per  unit  of  surface  may  be  increased. 


IO  MACHINE   DESIGN. 

Again,  consider  two  hubs,  one  of  steel,  the  other  of  cast  iron, 
both  on  the  same  steel  shaft,  with  p  and,  therefore,  d  the  same  in 
each  case.  In  the  former,  as  compared  with  the  latter,  the  cir- 
cumferential stress  S2,  the  radial  stress  Sv  and  the  unit  grip  pres- 
sure may  be  larger  and  the  allowance  may  be  increased,  although 
not  proportionately.  Therefore,  to  obtain  the  same  grip  in  both 
cases  there  should  be,  as  shown  by  (15),  a  decrease  in  the  value 
of  d,  p,  and  the  allowance  with  the  steel  hub. 

i.  ALLOWANCE. — With  regard  to  the  relative  values  of  shrinkage 
and  forcing  in  producing  grip,  the  meager  experiments  available 
indicate  that,  with  equal  allowances,  fits  of  the  former  type  are  the 
more  effective  in  resisting  both  torsional  and  axial  stresses.  This 
permits,  apparently,  for  the  same  unit  grip,  a  decreased  allowance 
in  shrinkage.  The  differences  in  grip  lie,  doubtless,  in  the  methods 
of  making  the  two  joints.  In  shrinkage,  there  is,  in  cooling,  sim- 
ultaneous contact  over  the  entire  area  of  clean  metallic  surfaces, 
without  relative  axial  movement  of  the  latter  except  that  due  to 
contraction,  while,  in  a  pressure  fit,  surfaces  lubricated  originally 
to  a  greater  or  less  extent,  are  not  only  abraded,  but  the  passage 
of  the  inner  member  produces  a  longitudinal  stress  within  the  in- 
ner layers  of  the  hub. 

If,  in  (15),  the  quantities  in  the  right-hand  member  be  kept 
constant,  there  will  be,  for  the  same  radial  pressure  and  grip,  a 
uniform  allowance  per  inch  of  diameter  for  shrinkage  or  forcing. 
This  uniformity,  while  by  no  means  universal,  is  the  practice  of 
many  large  companies,  a  frequent  allowance  for  steel  being  one 
one-thousandth  of  an  inch  (o.ooi  in.)  per  inch  of  diameter.  Since 
the  value  of  p  depends  upon  that  of  the  thickness,  there  must  be 
also  with  increasing  diameter  a  proportionate  growth  in  thickness. 
When,  as  in  Table  IV.,  there  is  a  decreasing  unit-allowance  with 
increased  diameter,  there  will  be  lessened  grip,  which  reduction 
must  be  met  by  an  augmented  length  of  hub.  In  any  case,  with 
diameters  of  2  inches  and  upward,  keys  should  be  fitted  between 
the  shaft  and  hub  as  an  assurance  against  slip. 

2.  LENGTH. — Let  P  x  R  —  driving  moment,  ^  =  polar  modu- 
lus of  section,  St  =  maximum  shearing  stress.  Then,  for  a  solid, 
cylindrical  shaft  of  diameter,  d : 

P  x  R  =  S.  x  Jc r  =  Ss  x  ~.  (16) 


SHRINKAGE   AND    PRESSURE  JOINTS.  II 

From  (62,  C)  : 

(17) 


Taking  St  and  5X  as  constant  and  equating  (16)  and  (17)  : 

l=Kd,  (i  8) 

where  Kisa.  constant.  Therefore,  with  a  constant  radial  stress,  the 
hub-length  should  vary  as  the  diameter,  in  order  to  make  the  grip 
equal  to  the  full  strength  of  the  shaft  in  torsion. 

3.  THICKNESS.  —  Let  Fig.  5  represent  the  transverse  section  of 
a  closed,  hollow  cylinder  (of  inner  and  outer  radii  R0  and  ^), 
initially  unstressed  but  subjected  to  the  internal  radial  pressure 
P0.  For  these  conditions,  equation  (23)  for  the  stress  t  at  radius 
R0  becomes  : 

/?  rr~,    D~ 

(19) 

from  which  it  appears  that,  if  t  =  P0  =  ultimate  tensile  strength, 
7?j  becomes  infinite,  i.  e.,  no  thickness  whatever  will  prevent  rup- 
ture. Further,  from  (64,  C),  P0  =  /  x  p,  and,  as  p,  in  an  initially 
unstressed  cylinder,  is  always  less  than  unity,  the  ultimate  tensile 
stress  t,  as  above,  will  be  reached  before  P0  attains  the  same  in- 
tensity. 

Again,  for  one  side  : 

Area  of  Load  Diagram  O-d-e-f  •=  P^R^  ; 

/•* 

Area  of  Resistance  Diagram,  a-b-c-d  =  I     tdr  =  P0J^0, 

J£0 

in  which  r  =  radius  of  any  point  within  the  wall  and  /  =  tensile 
stress  at  that  point,  as  given  by  (23).  It  is  apparent,  therefore,  that, 
for  any  given  values  of  P0,  R0,  and  the  ultimate  tensile  strength,  there 
is  but  one  value  of  ^  which  will  satisfy  the  equality  of  the  areas,  as 
above,  which  value  may  be  found  from  (19)  by  taking  t  at,  or 
within,  the  elastic  limit,  making  P0  <  /,  and  solving  for  Rr  With 
regard  only  to  adequate  strength,  no  useful  purpose  will  be  served 
by  increasing  the  value  of  ^  thus  obtained.  Finally,  by  substi- 

p 
tuting  p  =  y°  and  Sl  =  />„  in  (38,  C),  there  will  be  obtained  the 

total  allowance  for  the  prescribed  diameter. 


12  MACHINE   DESIGN. 

4.  FORM. — With  regard  to  the  form  of  the  contact-surfaces,  a 
slightly  tapering  hole  and  corresponding  inner  member  have  ad- 
vantages over  the  plain  cylindrical  shape,  in  that,  with  the  latter, 
the  entrance  of  the  hole  must  withstand  the  strain  of  abrading 
and  compressing  the  pin  or  shaft  throughout  the  length  of  the  fit. 
The  tapered  member,  on  the  contrary,  enters  without  contact  for  a 
considerable  distance  and  is  thus  well  guided ;  the  compression, 
upon  engagement,  is  distributed  over  a  greater  area ;  the  parts  are 
separated  readily  when  a  renewal  of  the  fit  is  desired ;  and  the 
drawings  may  be  marked  :  "  Fit  pin  —  inches  from  the  end  of  the 
hole,"  which  is  the  most  trustworthy  way  of  measuring  the  allow- 
ance. The  disadvantage  of  this  form  lies  in  the  difficulty  of  secur- 
ing, with  the  accuracy  required,  the  same  taper  in  both  members. 


3.     Metals. 

From  (9)  it  will  be  seen  that  the  radial  stress  of  the  inner  mem- 
ber and  the  circumferential  stress  within  the  outer,  depend  directly 
upon  the  modulus  of  elasticity  E  of  each  material  so  stressed. 
This  follows  since  E  is  a  measure  of  the  stiffness  of  a  metal,  i.  e.y 
the  stiffer  the  latter,  the  less  will  be  the  deformation  (strain)  under 
a  given  stress  and  the  larger  the  modulus.  The  following  are 
general  values : 

ELASTIC  LIMIT. 

Cast  Iron.  Wrought  Iron.  Steel. 

Tension 6,000  25,000  50,000 

Compression 20,000  25.000  50,000 

MODULUS  OF  ELASTICITY. 

Cast  Iron.        Wrought  Iron.          Steel. 

Tension 15,000,000        25,000,000  30,000,000 

Compression    . 15,000,000         25,000,000  30,000,000 

The  circumferential  stress  of  the  outer  member  is  the  important 
element,  especially  when  that  member  is  of  cast  iron,  a  metal  which 
has,  in  tension,  a  very  low  elastic  limit,  as  compared  with  that,  in 
compression,  of  the  steel  or  wrought  iron  of  the  inner  member. 
Cast  iron  is  also,  in  tension  especially,  a  very  uncertain  metal, 
owing  to  differences  in  composition,  in  the  size  and  form  of  the 


SHRINKAGE   AND    PRESSURE  JOINTS.  13 

casting,  and  in  the  intensity  of  the  original   shrinkage  strains. 
Professor  J.  B.  Johnson  gives  E  for  cast  iron  as  varying  from  — 

"  10,000,000  to  30,000,000  ;  but,  for  ordinary  foundry  iron,  it  may  be  taken  at  from 
12,000,000  to  15,000,000.  *  *  *  The  modulus  of  cast  iron  is  approximately  the  same 
in  tension,  compression  and  cross-bending."  * 

Professor  Burr,  in  commenting  upon  certain  tensile  tests  of  cast 
iron,  says  : 

"The  metal  is  seen  to  be  very  irregular  and  unreliable  in  its  elastic  behavior.  A 
large  portion  of  the  material  can  scarcely  be  said  to  have  an  elastic  limit,  although  no 
apparent  permanent  set  takes  place  under  a  considerable  intensity  of  stress.  In  other 
words,  although  perhaps  all  tested  specimens  resume  their  original  shape  and  dimen- 
sions for  small  intensities  of  stress,  yet  the  ratio  between  stress  and  strain  is  seldom 
constant  for  essentially  any  range  of  stress."! 


4.    Forcing  Pressures. 

The  pressure  required,  at  any  given  time  during  the  process,  of 
making  the  joint,  depends,  approximately,  upon  the  radial  stress, 
the  character  and  area  of  the  surfaces  in  contact,  and  the  coeffi- 
cient of  friction. 

1.  CHARACTER   OF   SURFACES. — This  will  vary  with  different 
metals  and  with  the  standard  of  workmanship.      If  the  surfaces  are 
smooth  but  not  accurately  of  the  same  form,  the  radial  and  forcing 
pressures  will  be  irregular  in  intensity.     With  rough  surfaces  the 
frictional  resistance  will  be  increased  ;  and,  in  extreme  cases,  longi- 
tudinal cutting,  uneven  bearing,  and  lessened  grip  may  follow. 

2.  COEFFICIENTS  OF  FRICTION.  —  In  a  pressure  fit  there  is  not 
only  surface  abrasion  but  the  material  of  the  outer  member  must 
be  forced  aside  by  the  forward  part  of  the  advancing  inner  mem- 
ber ;  and,  if  the  elastic  limit  of  the  softer  metal  be  exceeded,  some 
flow  of  the  latter  occurs.     The  resistance  is  not,  therefore,  purely 
frictional  and  the  usual  coefficients  of  friction  do  not  give  an  ac- 
curate measure  of  its  amount.     In  discussing  shrinkage  and  pres- 
sure fits,  Reuleaux  takes /=  0.2  which  is  the  value  used  by  Wei  s- 
bach  for  the  usual  metals  in  a  dry  state.     The  results  of  experiments 
presented  in  Table  I.  show,  as   a  rule,  much  lower  values  of/ 
than  that  quoted  above.     On  the  other  hand,  Rennie,  from  ex- 
periments upon  solids   usually   unlubricated,  gives,  for  pressures 

*  "  Materials  of  Construction,"  1898,  p.  476. 

f  "  Elasticity  and  Resistance  of  Materials  of  Engineering,"  1897,  p.  279. 


14  MACHINE   DESIGN. 

per  sq.  in.  ranging  from  i86|  to  560  Ibs.,  results,  for  the  coeffi- 
cient of  rest,  as  follows  :  * 

Wrought  iron  on  wrought  iron,  _/"=  0.25  to  0.41  ; 

Wrought  iron  on  cast  iron,  /=  0.28  to  0.37  ; 

Steel  on  cast  iron,  /=  0.30  to  0.36. 

Abrasion  occurred  in  the  first  case  at  672  Ibs.  pressure  ;  and,  in  the 
latter  case,  at  784  Ibs.  Broomall  f  gives,  for  static  friction,  as  above  : 

Cast  iron  on  cast  iron,  dry,  f=  0.3  1  14; 

Steel  on  cast  iron,  dry,  /=  0.2303  ; 

Steel  on  steel,  dry,  7=0.4408. 

Since  the  value  of  the  coefficient  is  affected  by  conditions  as  to 
motion  and  rest,  temperature,  lubrication,  and  speed  of  rubbing, 
reported  results  vary  considerably.  Both  shrinkage  and  forced 
fits  have  higher  radial  pressures  than  those  which  prevail  in  the 
usual  friction  tests  ;  the  resistance  in  forming  a  pressure  fit  is  not 
purely  frictional  ;  the  force  required  to  break  such  a  joint  may 
be  less  than  that  of  making,  if  the  elastic  limit  has  been  exceeded  ; 
and  pressure  fits  may  be  lubricated  only  to  the  extent  of  wiping 
the  surface  with  oiled  waste,  although  a  lubricant  of  white-lead 
and  oil,  mixed  to  the  consistency  of  paint,  is  frequently  used  to 
prevent  cutting.  In  view  of  these  conditions  the  application  to 
these  joints  of  the  usual  coefficients  for  unlubricated  metals,  is 
inadvisable. 

5.     Shrinkage  Temperatures. 

Let  e=  unit  diametral  or  circumferential  deformation  ;  «  =  coeffi- 
cient of  linear  expansion  for  a  change  of  one  degree  F.;  /=  number 
of  degrees  of  change.  Assume  an  outer  member  of  steel  with  an 
allowance  of  o.ooi  in.  per  inch  of  diameter  of  fit.  Then  (Fig.  4)  : 

e=r^        =  a.xt-     t=€-.  (20) 


Substituting  : 


0.0000065 

i.  e.,  a  raise  in  temperature  of  this  amount  would  give  the  mem- 
bers the  same  diameter.  The  usual  shrinkage-temperature  of 
wrought  iron  and  steel  is  about  600°,  the  increase  providing  for 
greater  allowance,  for  clearance  in  assembling,  or  for  both.  The 
value  of  a  for  cast  iron  is  0.0000062  per  degree  F. 

*Thurston,  "Friction  and  Lost  Work,"  1898,  p.  215. 
fLineham,  "  Mechanical  Engineering,"  1898,  p.  868. 


SHRINKAGE   AND    PRESSURE  JOINTS. 


6.    Shrinkage  vs.  Pressure  Fits. 

Table  I.  gives  the  results  of  comparative  tests  made  under  the 
supervision  of  Professor  Wilmore  *  upon  cast-iron  discs  which 
were  either  forced  or  shrunk  upon  steel  spindles,  the  latter  being 
pulled  from  the  discs  in  the  "  tension  "  tests  or  twisted  in  the  holes 
in  measuring  the  grip  in  torsion. 

TABLE  I. 


No. 

Fit. 

Test. 

Q 

* 

Si 

s, 

f 

I 

P 

Tension 

1,000 

O.OOI 

9,700 

10,116 

0-033 

2 

S 

" 

5,320 

" 

" 

" 

0.170 

3 

S 

" 

5,820 

" 

" 

a 

0.190 

4 

S 

Torsion 

2,200 

" 

II 

a 

0.072 

5 

P 

Tension 

2,150 

0.0015 

14,516 

15,275 

0.047 

6 

P 

Torsion 

2,200 

« 

0.048 

7 

P 

" 

2,800 

" 

II 

a 

0.061 

9 

S 

" 

9,800 

" 

'I 

a 

O.2IO 

10 

P 

Tension 

2,570 

O.OO2 

19,355 

20,366 

0.042 

ii 

S 

" 

7,500 

« 

" 

O.I  2O 

12 

S 

« 

8,100 

" 

" 

« 

0.130 

13 

P 

Torsion 

4,200 

« 

« 

•i 

0.069 

14 

P 

Tension 

4,000 

O.OO25 

24,^194 

25,458 

0.053 

15 

S 

" 

9,340 

" 

O.I  20 

16 

s 

« 

9,710 

II 

" 

ii 

O.I3O 

17     !      P 

Torsion 

4,600 

II 

" 

a 

O.06  1 

18           S 

" 

13,800 

II 

'I 

" 

O.igO 

19           S 

" 

17.000 

0.003 

29,000 

30,550 

0.190 

The  discs  were  6  in.  in  diameter  and  I  in.  thick,  with,  on  one 
side,  a  boss  2  in.  in  diameter,  projecting  ^  in.,  giving  a  bore  i^ 
in.  long  and  I  in.  in  diameter.  The  spindles  of  machinery  steel 
were  \\  in.  in  diameter,  turned  at  the  contact-surface  to  I  in. 
plus  allowance  for  a  length  of  i^  in.,  which  length  was  reduced 
by  a  taper  at  the  extremity  and  a  shallow  groove  at  the  top,  each 
^  in.  long,  making  the  bearing  surface  I  in.  in  length. 

The  number  of  spindles  tested  was  19.  The  diameter  of  the 
various  sets  differed  by  5  ten-thousandths  of  an  inch,  the  finished 
dimensions  being  i.ooi  in.,  1.0015  in.,  1.002  in.,  1.0025  in.  and 
1.003  m-  The  pressure  fits  were  made  without  lubrication,  other 
than  that  from  wiping  the  surfaces  with  oiled  waste.  The  spindles 
and  holes  were  found  to  be  in  good  condition  after  the  tests.  The 
maximum  force  required  to  move  each  spindle  is  given  as  Q  in  the 
table.  After  movement  had  occurred,  a  less  force  was  required 
to  continue  it  or  begin  it  anew.  Columns  Nos.  I  to  5,  inclusive, 

*  American  Machinist,  Feb.  16,  1899. 


16  MACHINE   DESIGN. 

of  the  table  were  taken  from  the  data  of  the  tests ;  the  values  in 
the  remaining  columns  were  computed  from  formulae  (15),  (38,  C), 
(62,  C)  and  (64,  C). 

Accuracy  in  calculating  the  intensities  of  the  stresses  ^  and  S2, 
and  the  coefficient  f,  is  to  some  extent  prevented  by  the  boss, 
groove,  and  taper  described  above.  The  approximation  given 
should  be,  however,  sufficiently  close  for  service.  The  value  of 

—  was  made  =  — —  =  5,  whence/-*  =  0.946.     Since  both  the  length 

and  diameter  of  the  contact  surface  =  I  in.,  (/>  =  allowance  in  each 
case.  The  coefficients  El  and  Ev  were  taken  as  30,000,000  and 
15,000,000  respectively.  Shrinkage  and  pressure  fits  are  marked 
respectively  "  S"  and  "  P,"  in  the  second  column  of  the  table. 

The  calculated  results  show  very  low  coefficients  of  resistance 
and  very  high  circumferential  stresses.  Since  the  ultimate  tensile 
strength  of  cast-iron  ranges  between  15,000  and  35,000  Ibs.  per 
sq.  in.  and  the  discs  were  of  good  quality,  rupture  of  the  inner 
layer  of  the  bore  did  not  occur ;  but  the  elastic  limit,  in  the  ma- 
jority of  the  tests,  was  exceeded.  The  superiority  of  the  shrinkage 
fit  is  marked,  as  is  also  that  of  both  types  in  torsion.  Excluding  tests 
Nos.  4  and  8,  the  results  give  average  ratios  of  strength,  as  follows  : 

Tension:  Shrinkage  to  Pressure  =  3.66; 
Torsion:  Shrinkage  to  Pressure  =  3.20; 
Shrinkage:  Torsion  to  Tension  =1.50; 
Pressure :  Torsion  to  Tension  —-  1.30. 

7.     Stationary  Engines :  Data  from  Practice. 

Prevailing  practice,  with  regard  to  diametral  allowances  in 
shrinkage  and  forced  fits  and  the  pressures  required  for  the  latter, 
varies  considerably,  owing  to  differences  in  the  sizes  of  the  mem- 
bers, the  qualities  of  the  metals,  the  workmanship  upon,  and  lubri- 
cation of,  the  contact-surfaces,  etc.  There  are  given  below,  in  tabular 
form,  through  the  courtesy  of  leading  manufacturers  of  stationary 
engines  and  similar  machinery,  records  of  allowances  as  follows  : 

Table  II.,  the  Lane  and  Bodley  Company ;  Table  III.,  the 
Russell  Engine  Company  ;  Table  IV.,  a  prominent  stationary  en- 
gine building  company ;  Table  V.,  the  Buffalo  Forge  Company; 
Table  VI.,  the  B.  F.  Sturtevant  Company  ;  Table  VII.,  summary 
of  Tables  II.  to  VI. 


SHRINKAGE   AND    PRESSURE   JOINTS. 


TABLE  II.* 


0 

2 

a.°^ 

O^S 

l>~ 

8 

Length  of  Fit 
un.). 

Mean  Diameter 
of  Hole 
(in.). 

Total 
Allowance 

S. 
j! 

< 

1    . 

& 

ft 

Volume  within 
Fitted  Surface 
(cu.  in.). 

Pressure  to 
Enter  Pin 
(tons). 

Pressure  at 
Mid-position 
(tons). 

Maximum  Pres- 
sure (tons). 

___ 

1.8798 

6.125 

1.8767 

.0031 

.0017 

36 

I6.7 

2 

10 

2O 

2 

1.8819 

6.I2S 

1.877 

.0042 

.0022 

36 

I6.7 

2 

15 

23 

3 

1.8774 

4-375 

1.8764 

.001 

.00052 

24.4 

13-7 

/2 

I 

4 

2-7455 

4-5 

2.7387 

.0068 

.00247 

38.7 

26.5 

3 

12 

25 

2.7465 

4-5 

2.7437 

.0028 

.001 

38.7 

26.5 

5 

12 

23 

6 

3.261 

5 

3-2542 

.0068 

.0021 

51 

41-5 

5 

2O 

45 

7 

3.2625 

5 

3-2555 

.007 

.002 

51 

41-5 

5 

IS 

30 

8 

3.267 

5 

3.261 

.006 

.0018 

51 

41-5 

5 

15 

20 

9 

4-2505 

6 

4.2402 

.0103 

.OO24 

79.8 

85.1 

5 

22 

44 

io 

4.2388 

6.625 

4.2478 

.0091 

.OO2I 

78.1 

93-4 

12 

30 

60 

ii 

4  2303 

6.5 

4.2224 

.co79 

.OOI9 

95-8 

91 

10 

60 

125 

12 

5-9343 

4.0625 

5.9216 

.0127 

.OO22 

75-7 

II2.2 

6 

16 

25 

13 

5-9381 

4 

5-9252 

.0129 

.OO22 

74-4 

IIO.4 

3 

18 

35 

14 

5-9294 

4-125 

5-9I94 

.01 

.OOI7 

76.7 

II3.8 

5 

15 

25 

15 

6.8829 

5-125 

6.8697 

.0132 

.002 

110.7 

I9O.I 

8 

20 

42 

16 

6.889 

5 

6.8785 

.0105 

.0015 

108 

185.9 

5 

22 

45 

X? 

6.8692 

4-875 

6.855 

.0142 

.O02I 

104.8 

180.4 

5 

35 

65 

18 

7.8884 

5-5 

7.873 

.0154 

.CO2 

135-9 

267.3 

5 

32 

64 

>9 

7.8715 

6-5 

78575 

.014 

.0018 

160.5 

3*5-9 

5 

25 

50 

20 

7.862 

5-625 

7.846 

.016 

.OO2 

138.2 

272.8 

8 

40 

80 

21 

8.924 

6.125 

8.905 

.019 

.OO2I 

170.8 

378.9 

20 

45 

68 

22 

8.9 

6-75 

8.8848 

.0152 

.OOI7 

188.4 

419.9 

5 

47 

96 

23 

8.878 

6-5 

8.8669 

.OII2 

.0013 

180.7 

401 

IO 

45 

92 

TABLE  III.* 
CAST-IRON  CRANKS. 


Total  Allowance,  In. 


In. 

Shrinkage. 

1'ressure. 

4      to    5 

0.0045 

o.o'  90 

5      '      7^ 

0.0030 

O.O060 

7/2  '      9 

0.0027 

0.0055 

10         '      12 

0.0025 

O.0050 

12         '      l6 

0.0020 

o.  0040 

16      «    18 

O.OOI5 

0.0030 

The  practice  of  the  B.  F.  Sturtevant  Company  is  as  follows  : 

(«•)  Shaft  couplings  are  bored  0.003  in-  less  than  the  shaft.  The  forcing  pres- 
sure ranges  from  6  tons  for  a  2lI3g-in.  shaft  to  12  tons  for  a  5~in.  shaft. 

(3)  Crank-pins  for  cast-steel  crank-plates  are  turned  0.005  m-  large.  The  forc- 
ing pressure  ranges  from  25  to  28  tons  for  a  5-in.  pin  to  10-15  tons  for  small  pins. 

(c)  Crank-pins  for  cast-iron  crank-plates  are  turned  0.009  m-  too.on  in.  large. 
The  forcing  pressure  is  as  in  (/>). 

(J)  Cast-iron  Counter-balance  Plates  shrunk  on  Steel  Crank- Discs.  For  diameters 
of  9  in.  to  II  in.,  the  total  allowance  is  0.007  m-  With  increased  diameters,  this 
allowance  decreases,  i.  <?.,  for  13-in.  diameter,  total  allowance  —  0.006  in. 

*  Machinery,  May,  1897. 


iS 


MACHINE   DESIGN. 
TABLE  IV. 


(A) 

(B) 

Diam.,  Shaft,  In. 

Allowance.  In.  of  Diam. 

Diam.,  Shaft,  In. 

Allowance,  In.  of  Diam. 

4 

0.003 

12 

O.OOI 

5 

0.0024 

13 

0.0009 

6 

O.OO2 

15 

0.0008 

7 

O.OOI7 

17 

0.0007 

8 

0.0015 

18 

0.0006 

9 

O.OOI3S 

19 

0.00055 

10 

O.OOI3 

22 

0.0004 

ii 

0.0012 

23 

0.00035 

12 

O.OII 

24 

0.0003 

13 

O.OOI 

26 

0.00025 

14 

O.OOI 

27 

O.OOO2 

15 

O.OOI 

16 

0.0009 

18 

o  0008 

20 

0.00075 

(A)  Steel  shaft  and  pin  to  cast-iron  cranks.     Average  pressure  required  =  12  5 
tons  (2,000  Ibs  )  per  in.  of  diam. 

(B)  Steel    shaft    to  cast-iron  wheel  hubs.     Average  pressure  required  =  10   tons 
(2,000  Ibs.)  per  in.  of  diam. 

TABLE  V. 


Pressure  Fits. 

Shrinkage  Fits. 

Diam.,      In. 

Total  Allowance,  In. 

Diam.,      In. 

Total  Allowance,  In. 

I    to      2 

O.OOI 

I    to      2 

0.009 

2 

3                        0.002 

2 

4 

O.OIO 

3 

5 

0.003 

4 

6 

I/64 

=  .0156 

5 

7 

0.005 

6 

9 

3/128 

=  -0234 

7 

10 

0.008 

9 

12 

1/32 

=  -0313 

10 

12            !                      O.OIO 

12 

18 

3/64 

=  .0469 

From  the  practice  of  the  B.  F.  Sturtevant  Company,  with  regard 
to  crank-plates  and  discs,  we  have  : 

TABLE    VI. 


Metal. 

Diameter. 

Allowance  Per  Inch. 

Type. 

Cast  steel. 

5  in. 

o.ooioo  in. 

Pressure. 

"     iron. 

5  " 

O.OO2OO     " 

<* 

«        « 

ii   " 

0.00064  " 

Shrinkage. 

"       " 

13  " 

0.00046   " 

" 

In  Table  II.  the  outer  member  of  No.  1 1  was  a  crank-disc  of 
cast  steel,  which,  with  less  allowance,  required  twice  the  maximum 
forcing  pressure  used  with  No.  10.  In  about  75  per  cent,  of  the 
fits,  the  maximum  pressure  was  twice  that  at  mid-position.  The 
allowance  for  shrinkage  in  Table  II.  is  one-half  that  for  pressure 
(§  2,  Allowance),  and,  in  both  types,  the  unit-allowance  decreases 
with  increased  diameter.  The  latter  is  true  also  of  the  fits  re- 


SHRINKAGE   AND    PRESSURE   JOINTS. 


TABLE  VII. 

SUMMARY. 


Diameter, 

Total  Allowance,  In. 

Members. 

Shrinkage. 

Pressure. 

Table  11. 

1.8798 

0.0031 

Shaft,  steel  ;  hub,  cast  iron. 

" 

4.2505 

0.0103 

«         « 

«<      <i      « 

" 

8.9000 

0.0152 

«         « 

«      «      « 

III. 

4      to    5 

0.0045 

O.OOgO 

Crank,  c. 

st  iron. 

» 

7-5  "     9 

0.0027 

0.0055 

" 

' 

« 

16    "  18 

0.0015 

0.0030 

" 

' 

IV. 

4 

O.OI20 

" 

'     shaft,  steel. 

" 

8 

O.OI2O 

M 

<        «         « 

V. 

16 

I      "       2 

O.009O 

0.0144 
O.OOIO 

" 

4    «     6 

0.0156 

11 

5    "     7 

O.OO5O 

" 

9    "  12 

0.0313 

«< 

10      "    12 

O.OIOO 

VI. 

5 

0.0050 

Shaft,  steel;  crank,  cast  steel. 

II 

5 

O.OIOO 

n       « 

"         "  iron. 

I 

ii 
13 

0.0070     \ 
0.0060      J 

Cast-iron      counter-balance 
plates  on  steel  crank  discs. 

corded  in  Table  IV.,  in  which,  further,  the  allowance  differs  with  the 
outer  member,  being  less  for  a  wheel  hub  than  for  a  crank,  owing 
doubtless  to  a  difference  in  the  thickness  of  the  metal  surrounding 
the  shaft.  The  allowance  and  length  of  hub  are  so  proportioned 
that  the  forcing  pressure  per  inch  of  diameter  is  about  uniform 
throughout  the  range  of  each  type.  In  Table  V.,  the  allowances  for 
pressure  fits  are  practically  uniform  per  inch  of  diameter,  while  those 
for  shrinkage  fits  decrease  with  increased  diameter.  The  latter 
also  exceed  considerably  the  corresponding  pressure-allowances. 
Table  VI.  gives  double  the  allowance  for  cast  iron  as  compared 
with  steel  and  a  decreasing  allowance  with  increased  diameter. 

8.     Marine  Engines  :   Data  from  Practice. 

In  marine  practice,  shrinkage  fits  are  used  in  assembling  "  built- 
up  "  crank-shafts  and  in  securing  the  bronze  casing  of  propeller- 
shafts.  Pressure  fits  are  employed  occasionally  with  crank-shafts 
and  frequently  with  smaller  work.  With  regard  to  shafts,  Mr. 
H.  F.  J.  Porter  says  : 

"  In  the  built-up  type,  the  various  parts  are  small  and  can  be  carefully  worked, 
and,  if  necessary,  bored  and  oil-tempered.  The  physical  properties  of  the  metal  can, 
therefore,  be  raised  to  the  highest  possible  limit.  The  forcing  or  shrinking  process, 
however,  always  puts  a  strain  on  the  metal  which  will  act  as  an  initial  load,  approach- 
ing possibly  close  up  to  the  elastic  limit.  In  the  solid  type,  on  the  contrary,  a  very 
large  ingot  would  be  required;  and,  as  such  a  crooked  forging  cannot  always  be  oil- 


20 


MACHINE   DESIGN. 


tempered  with  safety,  the  physical  properties  of  the  metal  cannot  usually  be  raised  by 
heat -treatment.  The  metal,  however,  can  be  relieved  of  all  strains  by  annealing;  and, 
if  properly  designed,  should  work  satisfactorily  against  externally  applied  stresses  for  a 
very  long  time. ' '  * 

When  it  is  possible  to  make  the  crank-shaft  in  sections  of 
moderate  length,  interchangeable  or  otherwise,  each  section  con- 
taining one  or  more  pairs  of  cranks,  these  sections  may  be  forged, 
each  from  a  single  ingot,  bored  and  oil-tempered,  thus  obtaining  high 
physical  characteristics  without  the  initial  stresses  due  to  building  up. 
The  necessity  for  casing  the  after,  or  propeller,  section  of  a 
marine  shaft  with  non-corrodible  material  lies  in  the  exposure  of 
that  section  to  the  action  of  sea-water,  both  in  the  "  stern -tube  " 
and,  sometimes,  beyond  the  latter  when  the  shaft  extends  through 
the  water  to  the  strut-bearing  and  propeller.  Within  the  tube  the 
bearings  are  of  lignum  vitae  and  the  lubricant  is,  as  a  rule,  sea- 
water,  the  forward  end  of  the  tube  being  closed  by  a  stuffing  box. 
To  prevent  corrosion  the  practice,  for  years,  has  been  (Fig.  6,  a, 
b]  to  encase  the  after  section  of  the  shaft  in  a  bronze  sleeve,  made 
in  short  (3 -ft.)  lengths,  shrunk  on,  with  lapped  and  recessed  joints, 
the  latter  being  sealed  on  the  outside  with  soft  solder.  Since  the 

torsion  of  the  shaft  tends  to 
loosen  the  casing,  the  latter  is 
secured  further  by  pins  or  tap- 
rivets.  The  casing  should  be 
recessed  within  the  propeller-hub 
and  should  make  an  absolutely 
water-tight  joint  with  the  latter. 
As  a  rule,  a  protecting  ring  of 
zinc  is  fitted  also  as  an  additional 
precaution  against  galvanic  action 
between  the  casing  and  shaft.  A 
less  usual  practice  than  the  use 
of  the  bronze  sleeve,  as  above,  is  to  leave  the  shaft  uncovered,  to  fit 
a  gland  at  the  after  end  of  the  stern-tube  and  to  keep  the  latter 
filled  with  oil  or  tallow.  In  U.  S.  Protected  Cruisers,  Nos.  20  to  22, 
the  diameter  of  the  propeller-shaft  is  18  in.  and  the  casing  thick- 
nesses are  I  in.  at  forward  and  i^g-  in.  at  after  bearing,  |  in.  at  the 
laps  (i  in.  long),  and  |-  in.  elsewhere.  The  following  data  are 
given  through  the  courtesy  of  leading  builders  of  marine  work. 

*"  Fatigue  of  Metal,"  &.c.,Jour.  Franklin  Institute,  Dec.,  1897. 


SHRINKAGE   AND    PRESSURE  JOINTS. 


2L 


AC.C 


fy.  « 


22  MACHINE    DESIGN. 

I.  The  practice  of  the  Midvale  Steel  Company,  Philadelphia, 
Pa.,  is  as  follows  : 

(#)  Shaft  Casings. — A  new  stern-tube  shaft  for  the  American 
Liner  New  York  was  made  recently  at  these  works.  It  was  40 
ft.  long,  20^  in.  diameter,  and  was  cased  partially  with  two  bronze 
sleeves,  each  8  ft.  long,  fitted  by  shrinkage,  the  total  allowance 
for  the  latter  bring  0.013  in.  =  0.000634  in.  per  inch  of  diameter. 
To  secure  uniform  expansion,  the  casing  was  set  vertically  and 
heated  internally  by  gas,  the  latter  issuing  from  a  pipe  a  little 
longer  than  the  sleeve,  inserted  within  the  latter,  and  perforated  for 
the  flow.  When  the  bore  as  gauged  showed  sufficient  expansion  for 
a  free  fit,  the  sleeve  was  slipped  in  place,  held  firmly  at  one  end,  and 
cooled  by  water  at  the  latter  until  contraction  and  grip  occurred. 

(£)  Crank-shafts. — An  allowance  of  o.ooi  in.  per  inch  of  diam- 
eter is  made  for  steel.  The  method  of  building  up  is  shown  in 
Figs.  7  to  1 6,  inclusive.  The  crank-pin  is  finish-machined  and  a 
cross-piece  (Fig.  9),  for  guiding  it  when  inserted,  is  secured  by 
screws  at  one  end.  The  holes  in  the  crank-webs  for  pin  and  shaft 
are  bored  in  a  vertical  machine  to  within  %  in.  of  finished  diameter, 
the  tool  (Fig.  7)  being  circumferential  and  two-bladed.  If  the  web 
is  less  than  7  in.  thick,  the  cut  is  made  from  one  side  in  one  setting ; 
otherwise,  it  is  run  half  way  through  from  each  face.  Then  the 
two  webs  which  form  a  pair  are  bolted  to  a  portable  surface-plate 
(Fig.  8),  the  latter  is  set  on  a  horizontal  machine,  and  the  holes  are 
bored  to  the  diameter  of  the  pin,  less  the  shrinkage-allowance. 
The  setting  on  the  plate,  with  regard  to  parallelism  and  distance, 
is  that  required  for  the  pin  when  the  latter  is  in  place. 

The  webs  are  then  heated  in  a  sheet-iron  furnace  (Fig.  10),  pro- 
vided with  a  burner  of  perforated  gas-pipe  (Fig.  1 1),  sliding  doors, 
and  covered  holes  for  occasional  measurement  of  the  bores  by  a 
gauge  (Fig.  12)  made  to  the  exact  diameter  of  the  pin,  the  gauge 
being  cooled  in  water  after  each  test.  When  the  expansion  is 
sufficient  for  a  free  fit,  the  webs  are  removed  from  the  furnace  and 
the  pin  is  pushed  home,  being  guided  by  the  cross-piece  so  that 
the  key-ways  come  flush,  the  latter  being  ensured  by  a  loose  false 
key  (Fig.  13)  which  is  inserted  as  soon  as  the  pin  enters  the  web. 
The  pin  is  slung  from  a  crane-hook,  the  sling  being  shifted,  if  the 
pin  is  solid,  when  the  latter  has  traversed  one  hole.  If  the  pin  is 
hollow,  it  rides  on  a  heavy  gas-pipe,  passing  through  the  bores 
and  suspended  by  slings  at  the  ends. 


SHRINKAGE   AND    PRESSURE  JOINTS. 


The  webs  and  pin  are  cooled  with  water,  the  false  key  is  taken 
out,  and  the  permanent  key  driven  home.  The  construction  is 
then  removed  from  the  surface-plate  and  set  in  a  horizontal  machine, 
where  the  holes  for  the  shaft  are  bored  to  the  finished  diameter, 
less  shrinkage-allowance.  The  webs  are  then  set  with  the  bores 
vertical  and  one  is  heated  as  before.  When  the  furnace  is  re- 
moved, a  planed  plate  (Fig.  14)  is  placed  under  the  heated  web,  a 
paper  liner — which  does  not  project  into  the  bore — is  laid  between, 
and  the  plate  is  forced  against  the  web  by  three  or  four  screw-jacks. 
The  shaft  is  then  slung  vertically  over  the  bore  and  lowered  until 
it  meets  the  plate,  the  downward  projection  due  to  the  liner  being 
sufficient  to  make  the  end  of  the  shaft  and  the  face  of  the  web 
flush,  when  cooled  by  water.  False  and  permanent  keys  are  fitted, 
as  with  the  pin.  While  lowering,  the  shaft  is  guided  by  a  wooden 
frame  (Fig.  15). 

The  remaining  portion  of  the  shaft  is  then  shrunk  into  the  other 
web  ;  the  completed  section  is  set  in  a  lathe  ;  the  shaft  and  pin  are 
tested  for  parallelism  ;  and  the  centers  of  the  shaft  are  drawn  to  cor- 
rect any  error.  The  section  is  then  finish-machined  and  joined 
by  shrinkage  with  others.  The  entire  shaft  is  then  placed  in  a  line 
of  V-blocks  (Fig.  16),  accurately  set  on  a  bed,  for  the  final  tests 
in  calipering,  parallelism  of  center-lines,  faces  of  webs  and  coup- 
lings, and  to  determine  whether  the  two  latter  are  square  with 
the  center-lines.  Any  errors  detected  are  corrected  by  hand- 
work. 

2.  Examples  of  the  practice  of  the  Union  Iron  Works,  San 
Francisco,  Cal.,  are  given  in  Table  VIII. 

TABLE  VIII. 


Members. 

Diam.  Ins. 

Total  Allowance. 

Forcing  Pres- 
sure, Tons. 

Shrinkage. 

Pressure. 

Steel  Crank  to  Steel  Shaft. 

14 

0.01562$ 

0.00938 

loo  to  150 

Wro't-iron  Crank  to  Wro't-iron  Shaft. 

8 

0.0125 

0.007 

80  "  100 

Cast-iron  Crank  to  (hard)  Steel  Shaft. 

8 

0.00938 

80 

"      «         »      «  (soft)        «         •« 

8 

0.00938 

20 

Wheel  Hub  (C.  I.  hard)       "        "1 
Length  of  Fit,  36-in.;  Mean  Dia'r.   J 

17-63/64 

0.003125 

80 

As  above  ;  hub  of  soft  cast  iron. 

0.003125 

3° 

Cylinder-Liner,  cast  iron,  hard.*       "^ 
In  Cylinder          "       "        medium,  j 

80 

O.O2I9 

As  above. 

60 

0.015625 

40  to  60 

«       « 

30 

0.0125 

Pressure  fits  now  discontinued. 


24  MACHINE   DESIGN. 

3.  The   practice    of  the    New    York    Shipbuilding    Company, 
Camden,  N.  J.,  is  as  follows  : 

(a)  Allowances. — These,  in  shrinkage  or  pressure  fits  in  iron  or 
steel,  are  one  one -thousandth  of  an  inch  (o.ooi  in.)  per  inch  of 
diameter  of  fit,  plus  one  one-thousandth  of  an  inch  (o.ooi  in.). 
Thus,  on  a  2-in.  diameter,  the  allowance  is  0.003  in.;  on  a  lo-in. 
fit,  o.o 1 1  in.,  etc. 

(V)  Form. — With  large  fits,  both  the  inner  and  outer  members 
have  a  taper  of  Jg  in.  to  the  foot,  the  allowances  being  as  above, 
If  the  conditions  are  such  that  it  is  more  convenient  to  ream  the  hole 
with  standard  parallel  reamers,  the  inner  member  is  tapered  one  half 
thousandth  of  an  inch  (0.0005  in.)  per  inch  of  length,  unless  the  fit 
is  so  long  that  this  taper  would  reduce  the  allowance  at  the  small 
end  to  less  than  one  half  that  at  the  other  extremity  of  the  joint. 

(c)  Drive  Fits. — For  these,  the  allowance  is  one  half  that  for 
shrinkage  or  pressure  joints. 

(d)  Shaft-Casings. — The  allowance  is  one  half  that  for  a  shrink- 
age fit  on  heavy  work. 

4.  The  Harlan  and  Hollingsworth  Company,  Wilmington,  Del., 
give,  in  built-up  shafts,  a  shrinkage  allowance  of  one  one-thou- 
sandth of  an  inch  (o.ooi  in.)  per  inch  of  diameter;  and,  in  shaft- 
casings,  one  half  of  this  amount,  i.  e.,  0.0005  m- 


9.     Railway  Work:   Data  from  Practice. 

In  railway  work  pressure  fits  are  used  in  securing  wheels  to 
axles  and  crank-pins  to  driving  wheels  while  the  tires  of  the  lat- 
ter are  shrunk  in  place.  A  pair  of  drivers  consists  of  the  axle  of 
wrought  iron  or  steel,  the  wheel-centers  of  cast  iron,  the  tires  of 

TABLE  IX. 


Total  Allowance,  Tire,  In. 

A 

B 

38 

0.040 

0.0312=1/32 

44 

0.047 

0.0469  =  3/64 

So 

0-053 

0.0625  =  1/16 

£ 

O.o6o 
O.o66 

0.0625  =  1/16 
0.0781  =  5/64 

66 

0.070 

0.0781  =  5/64 

steel,  and  the  crank-pins  of  the  latter  metal.     In  assembling  these 
parts,  the  wheel-centers  are  first  driven  on  the  axles  and  keyed. 


SHRINKAGE   AND    PRESSURE  JOINTS. 


The  tires  are  then  shrunk  on,  the  holes  bored  for  the  crank -pins 
and  the  latter  pressed  in.  Finally,  the  tires  are  turned  to  the  fin- 
ished size. 

1.  TIRES.  —  In   1886-7  the  American   Railway's  Master  Me- 
chanics' Association  recommended  and  adopted  the  diameters  and 
allowances  printed,  through  the  courtesy  of  that  Association,  in 
the  first  and  second  columns  of  Table  IX.     These  allowances 
have  not  met  universal  use ;  and,  in  column  B  the  practice  of  a 
prominent  road,  for  the  same  diameters,  is  presented.     The  fit  is 
cylindrical  between  the  wheel-center  and  the  tire.     The  latter  is 
heated  usually  by  gas-jets  set  about  its  circumference  ;  and,  when 
expanded,  is  placed  on  the  wheel-center  and  allowed  to  cool. 
Tires  thus  secured  resist  the  lateral  thrust  and  rolling  action  until 
they  are  worn   considerably,  when  they  may  become  loose  and 
require  liners  or  refitting. 

2.  WHEEL-FITS. — The  joint  is  cylindrical.     The  pressure  re- 
quired for  mounting  the  wheel  is  usually  9  to  i  o  tons  per  inch  of  di- 
ameter of  fit;  for  removal,  the  total  pressure  may  be  100  to  150 
tons,  depending  on  the  condition  of  the  joint  as  to  rust,  etc.     The 


FIG.    17. 

mechanism  used  in  these  operations  is  shown  by  Figs.  17  and  18, 
which  represent  the  4<DO-ton  wheel-press  made  by,  and  illustrated 
herein  through,  the  courtesy  of  the  Niles  Tool  Works  Company, 
Hamilton,  Ohio. 

The  press  consists  essentially  of  a  hydraulic  ram  ;  a  resistance 
head,  or  abutment,  sliding  on  tension-bars  to  which  it  may  be 
keyed  at  the  required  distance  from  the  ram-head  ;  and  supporting 


26 


MACHINE   DESIGN. 


hooks  for  the  axle,  depending  from  the  upper  bar.  The  resistance- 
head  has  a  central  bearing  for  the  axle,  to  enable  the  latter  to  lie  in 
the  line  of  pressure.  In  mounting  wheels,  the  axle,  with  each  wheel 
started  on  its  fit,  is  hoisted  into  the  hooks  and  resistance-head,  and 
the  ram,  acting  on  the  hub  next  to  it,  drives  both  wheels  home. 
In  dismounting,  the  resistance-head  is  moved  nearer  to  the  ram, 
the  stop-block  shown  in  the  head  is  removed,  and  the  axle  is  laid 
within  the  latter.  The  ram  then  engages  the  axle  and  forces  it 
out  of  the  wheel,  after  which  the  axle  is  reversed  and  the  remain- 
ing wheel  removed  in  a  similar  way. 


FIG.  18. 


The  ram  R  is  a  solid  iron  casting,  provided,  at  the  rear,  with 
cupped  leather  packing.  The  cylinder  is  of  strong  and  dense  cast 
iron,  lined  with  \  in.  copper,  the  latter  being  spun  into  place 
and  beaded  over  the  counterbore.  Water  from  the  pumps  en- 
ters at  d;  a  release-valve  f,  operated  by  a  hand-wheel,  permits 
the  fluid  to  escape,  when  desired,  into  the  tank  ;  a  safety-valve,  e, 
limits  the  pressure  to  6,000  Ibs.  per  sq.  in.;  and  the  chains  and 
counter-weight  retract  the  ram  when  the  release  valve  is  opened. 

The  pump  is  provided  with  two  plungers,  if  in.  and  I  in.  diam- 
eter, respectively,  each  operated  by  an  eccentric  on  the  driving 


SHRINKAGE   AND    PRESSURE  JOINTS.  2/ 

shaft.  The  plunger  chambers  are  separate,  each  being  provided 
with  suction  and  discharge  valves.  Through  the  suction  pipe  to 
each  chamber  a  tripping  rod,  c,  passes,  which,  when  elevated,  lifts 
the  suction  valve  from  its  seat  and  thus  stops  the  delivery  from 
that  chamber  while  the  shaft  still  rotates.  The  rod,  c,  is  connected 
externally  to  a  lever  and  link,  a  support  holding  the  latter  in  place 
when  the  suction-valve  is  operating.  It  will  be  seen  that  the  trip- 
ping rods  provide  a  very  quick  method  of  throwing  either  or  both 
pumps  out  of  operation — an  action  which  is  essential,  since,  when 
the  wheel  has  reached  the  end  of  the  fit,  the  inflow  to  the  cylinder 
should  cease  at  once. 

In  starting  the  press,  the  belt  is  shifted  to  the  tight  pulley,  the 
trip-rods  are  lowered  and  both  plungers  operate  until  such  a  pres- 
sure has  been  obtained  as  the  belt  permits.  Then  the  suction 
valve  of  the  larger  chamber  is  tripped  and  the  work  continues 
with  the  smaller  plunger  until  the  limit  of  the  fit  is  reached,  when 
the  remaining  suction  valve  is  raised  and  further  movement  of 
the  ram  is  prevented. 

10.     Shrinkage  in  Gun  Construction. 

The  stresses  to  which  a  gun  is  subjected  upon  the  explosion 
of  the  charge  are  :  First,  a  radial  pressure  tending  to  split  it  on 
an  axial  plane  ;  and  second,  a  longitudinal  stress  acting  to  rupture 
it  on  a  plane  transverse  to  the  axis.  There  must  be  considered 
also  in  design  the  radial  compression  of  the  bore — due  to  the 
shrinkages  of  the  exterior  cylinders  —  which,  when  the  system  is 
at  rest,  the  inner  layer  must  withstand. 

To  secure  equal  strength  throughout  without  undue  weight,  the 
material  should  be  so  arranged  that  every  portion  does  its  full 
share  in  resisting  the  pressure  from  within.  Fig.  5  shows  the 
rapid  reduction  in  stress  toward  the  exterior  of  a  homogeneous 
cylinder,  the  tension  in  the  outer  layer  being  but  two  fifths  of  that 
in  the  inner,  when  ^  =  2R0.  This  uneconomical  distribution  of 
the  metal  and  the  fact  that  the  elastic  strength  of  the  latter  is,  in 
such  cylinders,  the  limit  of  the  allowable  internal  pressure  PQ,  led 
to  the  abandonment  of  cast  guns,  although  some  measure  of  com- 
pressive,  reinforcing  stress  upon  the  bore  may  be  obtained,  during 
casting,  by  cooling  the  inner  wall  first,  thus  producing  tension  in 
the  outer  layers. 


28  MACHINE   DESIGN. 

Maximum  economy  of  material  will  be  attained  when  the 
stresses  throughout  the  walls  are,  at  all  points,  upon  the  explosion 
of  the  charge,  not  only  approximately  equal  but  also  the  greatest 
permitted  by  the  elastic  strength.  This  condition  can  be  ap- 
proached only  by  placing  the  outer  metal  in  a  state  of  initial  ten- 
sion, the  result  being,  when  the  system  is  at  rest,  a  compression 
and  reinforcement  of  the  inner  layer,  the  latter  being  given  thus 
additional  strength,  since  the  initial  compression  must  be  over- 
come by  the  pressure  of  the  gases  before  tensile  stress  in  the 
fibers  will  be  produced.  In  order  to  develop  these  initial  stresses, 
the  gun  is  built  of  separate  concentric  cylinders  shrunk  one  upon 
the  other,  the  unit  diametral  allowance  or  relative  shrinkage  of  the 
outer  cylinders  being  such  that,  while  these  cylinders  are  thus 
normally  in  tension,  they  have  still  a  margin  of  strength,  within 
their  elastic  limits,  to  withstand  the  added  tensile  stress  upon  ex- 
plosion. The  stress-diagrams  for  such  a  construction  are  shown 
approximately  in  Fig.  5,  a,  which  represents  a  portion  of  a  trans- 
verse section  of  a  tube  with  superposed  cylinder.  The  area, 
a-b-c-d,  is  the  diagram  of  tangential  stress  for  a  single  cylinder  of 
the  maximum  radius  and  combined  thickness,  subjected  to  the 
internal  pressure,  P0.  The  area,  e-g-f-c,  represents  the  initial 
tension  in  the  outer  cylinder,  and  its  equivalent,  d-e-h-k,  the  initial 
compression  in  the  tube.  The  areas,  d-l-g-e  and  e-m-n-c,  show, 
respectively,  the  tangential  stresses  in  the  tube  and  cylinder  when 
under  the  internal  pressure,  P0.  It  is  obvious  that  the  latter 
areas  are  together  equal  to  the  original  diagram,  a-b-c-d,  less  that 
of  initial  compression,  and  plus  that  of  initial  tension.  The 
possibility  of  reducing  the  stress  at  the  bore  is  apparent. 
Since  both  radial  and  circumferential  stresses  change  with  each 
increment  of  radius,  the  greater  the  number  of  superposed 
cylinders  in  a  given  thickness,  the  more  equable  will  be  the 
disposition  of  stress  under  internal  pressure.  In  practice  (Fig. 
19),  the  number  of  such  cylinders  is,  in  large  guns,  four,  viz. : 
the  tube,  a  single  forging,  the  length  of  the  bore ;  the  jacket, 
encircling  the  tube  from  the  breech-end  about  half  way  to 
the  muzzle ;  two  layers  of  hoops,  superposed  upon  the  jacket, 
the  chase-hoop  extending  to  the  muzzle  ;  and  tapering  and 
locking  bands.  With  regard  to  the  radial  and  circumferential 
stresses  in  a  gun  thus  assembled,  Major  Rogers  Birnie,  U.  S.  A., 
says : 


SHRINKAGE   AND    PRESSURE  JOINTS.  29 

"  The  accepted  theory  of  this  mode  of  construction  is  to  assemble  the  several  rows 
of  cylinders  so  that  : 

"  In  whatever  state  the  system  may  be  considered,  none  of  the  fibers  of  any  cylinder 
in  the  structure  shall  be  elongated  or  contracted  beyond  the  elastic  limits  determined 
for  such  displacements  by  the  free  tests  of  the  metal. 

"  With  the  system  at  rest  this  applies  especially  to  the  tube  which,  ordinarily,  has  to 
support  alone,  or  without  other  assistance  than  the  atmospheric  pressure,  the  accumu- 
lated stress  due  to  the  shrinkages  of  all  the  outside  cylinders.  Under  these  circum- 
stances, the  surface  of  the  bore  undergoes  the  greatest  change  of  form  by  compression, 
so  that  the  shrinkages  of  the  outer  cylinders  must  be  limited  to  retain  uninjured  the 
elastic  properties  of  the  metal  at  the  surface  of  the  bore  of  the  tube.  (It  is,  perhaps, 
an  open  question  whether  the  compression  of  the  bore  may  not,  with  advantage,  be 
carried  beyond  this  limit ;  but,  for  the  purposes  of  theoretical  discussion,  we  assume 
that  it  should  not  be. ) 

"  With  the  system  in  action,  that  is,  subjected  to  the  maximum  interior  pressure  which 
it  can  support  with  safety,  the  cylinders  or  hoops  composing  each  layer  of  the  structure 
should  work  together  to  the  elastic  limit  of  their  metal.  Here,  again,  it  is  the  interior 
fibers  which  undergo  the  greatest  change  of  form  in  general  by  circumferential  exten- 
sion in  the  outer  cylinders  and  by  radial  compression  in  the  inner  cylinders.  The  theo- 
retical resistance  of  the  gun  must  then  be  limited  to  retain  uninjured  the  elastic  proper- 
ties of  the  metal  at  the  interior  of  any  of  the  cylinders  composing  the  structure.  This 
involves  the  following  considerations,  viz.  :  As  many  of  the  cylinders  as  practicable 
should  work  together  to  the  elastic  limit  of  their  material  under  extension  ;  but,  when 
other  cylinders  are  endangered  from  radial  compression  of  their  walls,  the  theoretical 
interior  pressure  must  be  curtailed  to  provide  against  such  over-compression,  and  the 
working  tensions  of  the  first-named  parts  will  be  correspondingly  reduced.  However, 
the  wall  of  the  tube  (or  part  of  the  structure  next  to  the  bore)  has  always  to  support 
the  greatest  normal  pressure  with  the  system  in  action  ;  hence,  frequently,  in  this  state 
of  the  system  also,  the  theoretical  resistance  of  the  gun  will  be  limited  by  the  strength 
of  the  tube  to  resist  compression,  in  this  case  radial  instead  of  tangential,  as  in  the 
other  extreme  state  of  the  system."  * 

Major  Birnie  considers  that  the  longitudinal  tension  developed 
in  firing  may,  without  noteworthy  error,  be  neglected  in  deducing 
the  equations  of  equilibrium,  expressing  the  relations  between  the 
tangential  and  radial  resistances  for  any  state  of  the  system. 

i.  SHRINKAGE  FORMULA. — For  the  deduction  which  follows 
the  author  is  indebted  to  Professor  Philip  R.  Alger,  U.  S.  N., 
formerly  of  the  Bureau  of  Ordnance,  U.  S.  Navy,  now  head  of 
the  Department  of  Mechanics,  U.  S.  Naval  Academy.  Practically 
all  of  the  guns  in  the  U.  S.  Navy  were  assembled  with  shrinkages 
calculated  by  the  formulae  given  below. 

In  this  deduction  it  is  assumed  : 

i.  That  there  is  no  longitudinal  stress  on  any  layer.  This 
would  be  true  only  in  the  case  of  a  hollow  cylinder  under  fluid 


*  Ordnance  Department  U.  S.  A.,  "Notes  on  the  Construction  of  Ordnance,"  No.  35. 


30  MACHINE   DESIGN. 

pressure  and  having  both  ends  free,  and  is  not  true  for  a  gun  ;  but, 
even  with  the  latter,  only  the  layer  in  which  the  breech-plug  houses 
is  under  direct  longitudinal  stress  and  that  stress  diminishes  rapidly 
as  we  go  forward  from  the  breech -plug  face. 

2.  That  a  transverse  section  of  the  cylinder  when  at  rest  re- 
mains a  plane  normal  to  the  axis  of  the  cylinder  when  the  latter  is 
under  strain — in  other  words,  that  the  longitudinal  strain  is  uniform 
over  the  whole  section.     This  would  be  a  natural  result  of  the 
condition  of  free  ends,  but  can  be  considered  as  only  approximately 
true  for  a  gun. 

3.  That  the  total  strain,  in  any  direction,  due  to  all  the  stresses 
is  the  measure  of  the  tendency  to  yield  in  that  direction,  so  that 
the  limit  of  safety  is  reached,  not  when  the  stress  in  any  direction 
equals  the  elastic  strength  of  the  material,  but  when  the  strain  in 
any  direction  equals  the  strain  which  would  be  caused  by  the  direct 
action  of  a  single  stress  equal  to  that  elastic  strength. 

4.  The  ratio  of  strain,  in  the  direction  of  the  stress  producing 
it  to  the  accompanying  strain  at  right  angles  to  that  direction,  is 
taken  to  have  the  value  3. 

(a)  Stresses  and  Strains. — Let  a  hollow  cylinder  of  radii  R0  and 
7?j  be  under  pressure  P0  from  within  and  Pl  from  without,  and 
let  T0  and  7^  be  the  resulting  circumferential  tensions  at  the 
inner  and  outer  surfaces.  Also,  let  /  and  /  be  the  circumferential 
tension  and  radial  pressure  at  any  point  of  radius  r  within  the 
cylinder-wall  and  let  et,  er  and  et  be  the  tangential,  radial  and 
longitudinal  strains  at  the  same  point.  Also,  let  E  be  the  modulus 
of  elasticity  of  the  material.  Then  : 


and  since,  by  hypothesis,  et  is  constant,  we  have 

/  —  p  =  constant  =  k. 
But 


'A> 

and,  assuming  /=//(r),  this  gives, 


SHRINKAGE   AND    PRESSURE   JOINTS. 


whence 


f(r)=-pr-    and  so,  t=f'(r)=-p-r^. 

Thus,  we  have  t  —  p  =  k  and  /  -f  p  =  —  r  -r*  whence 

dp 


the  integration  of  which  gives  2p  +  k  =  -\t  where  kv  is  a  constant 

fcZ 

of  integration.      Combining  with  t —p  =  k,  we  have  t+p=^\. 

These,  then,  are  the  fundamental  equations  which  express  the 
relation  between  circumferential  tension  and  radial  pressure  at  all 
points  within  the  cylinder  : 

t-p=k=T0-PG=Tl-Pl  I 

(/ + py  =  **  =  (TO  +  />x*  =  (T.  +  piW 1 

Eliminating  7j  between  the  last  parts  of  these  equations,  we  have  : 


and  substituting  this  in  the  first  parts  of  the  same  equations,  we 
have,  after  combining  : 


, 


-R02 


(23) 


Substituting  these  values  in  the  first  part  of  (21),  we  have,  for 
the  tangential  strains  at  the  inner  and  outer  surfaces,  where  r  =  R0 
and  r  =  Rv  respectively  : 


(24) 


Suppose  now  the  pressure  Pl  to  be  caused  by  a  second  cylinder 
(radii  Rl  and  /?,)  embracing  the  first  and  itself  under  the  external 


MACHINE   DESIGN. 


pressure  Py  Let  the  circumferential  tension  at  its  inner  surface 
be  designated  as  Zj'  (to  distinguish  it  from  Tv  the  tension  of  the 
outer  surface  of  the  inner  cylinder,  which  is  under  the  same  radial 
pressure  Pv  but  not  at  the  same  tension  as  the  surface  in  contact 
with  it)  and  that  at  its  outer  surface  as  T2.  Then,  applying 
formula  (24)  to  this  second  cylinder,  we  have,  for  the  circumferen- 
tial strains  at  the  inner  and  outer  surfaces  : 


(25) 


Finally,  assuming  P2  to  be  caused  by  a  third  cylinder  (radii,  R2 
and  R^)  whose  outer  surface  is  under  no  pressure,  we  have,  for  the 
circumferential  strain  at  its  inner  surface : 


tr. 


(26) 


Now  let  -£,  -£. ,  and  ^   be  the  values  fixed  for  the  maximum 

strains  of  the  three  cylinders  respectively,  when  under  the  action 
of  the  system  of  pressure  P0,  /*,  and  Py  Substituting  these  values 
for  eTo,  eTl,,  and  eTz,  in  (24),  (25),  and  (26),  we  have 


(27) 


22  -f  2R? 


the  last  of  which  equations  gives  the  internal  pressure  which  the 
built-up  cylinder  will  stand,  if  its  parts  have  been  so  assembled 
that  the  inner  surface  of  each  reaches  at  the  same  instant  the  con- 
dition of  maximum  circumferential  strain  assigned  to  it.  This,  of 
course,  implies  a  definite  shrinkage  for  each  cylinder,  which  shrink- 
age remains  to  be  determined. 

(&)  Relative  Shrinkages. — Observe  now  that  equations  (24),  (25) 
and  (26)  give  the  tangential  strains  resulting  from  the  pressures  P0, 


SHRINKAGE   AND    PRESSURE  JOINTS.  33 

Pv  and  P2,  and  that  if  we  substitute  for  these  pressures  any  simul- 
taneous changes  in  their  values  as  pQ,  pv  and  /2,  the  same  equations 
will  give  the  corresponding  changes  of  strain.  But  the  surfaces  of 
contact  of  the  cylinders  must  contract  and  expand  together  and  so 
the  change  of  strain  at  the  outer  surface  of  each  cylinder  must  equal 
that  simultaneously  occurring  at  the  inner  surface  of  the  cylinder 
embracing  it.  Hence  equating  the  second  part  of  (24)  to  the  first 
part  of  (25)  and  the  second  part  of  (25)  to  (26),  after  replacing 
P0,  Pv  and  P2  by  pv  /,  and  pv  we  have  : 


-  R*  (R*  -  R*)fi  +  R>(R>  -  R^  =  0  1 

R?  (R?  -  Rfip,  -  R;  (X*  -  R?}pz  =o  J    ' 

the  first  of  which  gives  the  relation  between  simultaneously  occur- 
ring changes  in  the  pressures  at  the  radii,  Rti,  Rv  and  Rv  and  the 
second,  the  relations  between  such  changes  at  the  radii,  R^  and  Rr 
If,  now,  in  the  first  equation  of  (28),  we  make  p0  =  —  P0  and 
P2  =  —  P2,  we  find  : 

R?  (R*  -  X*)  P9  +  R*  (X*  -  Rf).Pj 
l~  ^i2W-^o2) 

and  this  is  the  change  of  pressure  at  the  radius  Rlt  which  would 
result  from  the  simultaneous  removals  of  the  outer  cylinder 
which  causes  P2  and  of  the  internal  pressure  P0  itself.  There- 
fore, substituting  this  value  of  p{  for  Pl  and  —  P2  for  P2  in  the 
second  equation  of  (25),  we  have,  for  the  change  of  outer  diameter 
of  the  middle  cylinder,  due  to  removing  the  outer  cylinder  and 
suppressing  the  internal  pressure,  the  expression  : 


But,  by  hypothesis,  the  strain  at  the  inner  surface  of  the  outer 

/i 

cylinder,  before  the  change  just  referred  to,  was  -£,  and,  there- 
fore, the  relative  shrinkage  of  the  outer  cylinder  must  have  been  : 


To  find  <pv  the  relative  shrinkage  of  the  middle  cylinder,  put 
—  P0  for  P0  and  —  Pl  for  Pl  in  the  second  equation  of  (24)  which 


34  MACHINE   DESIGN. 

gives,  for  the  change  in  outer  diameter  of  the  inner  cylinder,  due 
to  removing  the  outer  cylinders  and  suppressing  the  internal  pres- 
sure, the  expression  : 


whence 


By  the  term  relative  shrinkage  is  meant  the  difference  of  diameter 
per  unit  length  of  diameter  of  the  surfaces  to  be  superposed,  so 
that  the  actual  differences  of  diameter  are  zR2<p2  and  2Rly>l. 

(c)  The  Method  of  Procedure,  then,  is  to  calculate  Pv  P1  and  P0  by 
formulae  (27)  and  then  determine  the  shrinkages  by  formulae  (29) 
and  (30).  It  may  be,  however,  that  the  shrinkages  thus  found 
would  cause  excessive  compression  of  the  bore  of  the  inner  cyl- 
inder, when  at  rest  ;  and,  if  so,  smaller  values  of  6l  and  62  must 
be  used.  To  ascertain  whether  this  is  the  case,  eliminate  p2  be- 
tween the  parts  of  equation  (28)  which  gives  : 


'A  J 


and,  making  /0  =  —  P0  in  this,  the  resulting  value  of  p^  is  the 
change  of  pressure  at  the  outer  surface  of  the  inner  cylinder  due 
to  the  suppression  of  PQ.  Therefore,  pv  +  Pl  must  be  the  pressure 
on  that  outer  surface  when  the  system  is  at  rest  ;  and  this  must 
not  exceed 


since,  if  it  does,  the  tangential  compression  of  the  bore  will  ex- 
ceed 00. 

As  a  matter  of  fact,  however,  experience  seems  to  show  that 
there  is  no  objection  to  compressing  the  bore  beyond  the  elastic 
limit  of  the  material  under  tension,  presumably  because  the  elas- 
tic resistance  to  compression  is  really  considerably  greater  than 
that  so-called  elastic  limit  of  tension. 

It  is  also  to  be  noted  that  no  account  has  been  taken  of  the  fact 
that  the  radial  strain  at  the  inner  surface  of  a  cylinder  may,  and 


SHRINKAGE   AND    PRESSURE  JOINTS.  35 

indeed  sometimes  does,  exceed  the  tangential  strain,  while  our 
formulae  assume  that  it  is  only  the  latter  which  must  not  exceed  a 
fixed  limit.  This,  too,  can  only  be  justified  by  the  assumption 
that  the  material  really  has  a  higher  limit  of  elasticity  under  com- 
pression than  under  tension. 

In  assembling  U.  S.  naval  guns  with  shrinkages  calculated  by 
the  foregoing  formulas,  #0,  dl  and  02  were  taken  as  the  lowest 
elastic  limit  given  by  any  specimen  from  the  particular  forging 
considered,  excepting  where  the  resulting  compression  of  bore 
considerably  exceeded  #0,  in  which  case  0t  and  02  were  some- 
what reduced.  The  formulae  as  given  herein  are,  of  course, 
easily  extended  to  cover  cases  where  there  are  more  than 
three  layers. 

The  tangential  strain  is  really  the  change  of  length  per  unit 
length  of  the  circumference  and,  so  also,  the  change  of  length  per 
unit  length  of  diameter.  An  alternative  nomenclature  of  the 
strains  is  as  follows:  Take  a  circle  of  radius  'r  in  the  cylinder 
walls  when  at  rest  and  suppose  that,  when  the  pressures  act,  each 
point  of  the  circle  moves  outwardly  Jrand  axially  Ah,  then  the  tan- 

Jr  dAr 

gential  strain  is  — ,  the  radial  strain  is  -j-,  and  the  longitudinal 

strain  is  --,,  ,  these  strains  being  what  have  been  called  et,  er  and  ev 

(d}  Radii. — If  only  the  tangential  resistance  to  internal  pressure 
is  to  be  considered,  the  maximum  value  of  P0  will  be  obtained  by 
making  the  radii  increase  in  geometrical  progression  from  that 
of  the  chamber  outward,  provided  the  several  cylinders  have  the 
same  elastic  strength  and  the  same  modulus  of  elasticity.  Thus, 
for  the  case  of  one  cylinder  superimposed  upon  another,  make  P0, 
formula  (27),  a  function  of  Rl  (R0  and  R2  being  constant  and 

6l  =  0Q),  differentiate,  and  make  -^  =  o.     After  cancellation,  we 

have  R*  =  R0R2,  showing  that  the  maximum  value  of  elastic  re- 
sistance for  a  given  total  thickness  of  a  given  material  occurs  when 
the  radius  of  the  common  surface  is  a  mean  proportional  between 
the  inner  and  outer  radii.  For  example,  with  the  6-inch  gun  of 
4-inch  chamber-radius  and  8-inch  thickness  of  chamber-wall,  the 
maximum  resistance  against  tangential  bursting  stress  would  be 
secured  by  making  R0  =  4-inch  ;  /?t  =  4^3  ;  R2  =  4^9  ;  and 
^3=4^27=  12. 


36  MACHINE   DESIGN. 

In  practice,  however,  other  considerations  than  tangential 
stress  prevent  complete  conformity  with  theory.  In  the  first 
place,  it  is  necessary  to  make  that  layer  which  takes  the  longitu- 
dinal strain  of  sufficient  cross-section.  In  United  States  guns,  the 
breech-block  houses  in  the  jacket  or  second  layer  and  the  area 
~(R£  —  T^2)  must  be  adequate,  being,  in  naval  guns,  about  three 
times  that  of  the  rear  end  of  the  chamber,  so  that  the  longitudinal 
stress  on  the  jacket,  if  uniformly  distributed,  is  one  third  of  the 
chamber  pressures.  In  French  guns,  the  breech-block  usually 
houses  in  the  tube  or  inner  layer,  thus  making  Rl  much  greater 
than  is  necessary  for  resistance  to  the  maximum  tangential  stress. 
Again,  the  tube  thickness  over  the  enlarged  chamber  should  not  be 
too  small  to  prevent  lining  the  bore  with  a  thin  tube,  after  the  erosion 
of  the  powder  gases  has  cut  away  the  rifling  and  rendered  the  gun 
inaccurate.  Finally,  the  necessity  for  keeping  down  weight,  which 
prescribes  a  decreasing  exterior  diameter  to  correspond  with  the 
diminishing  pressure  toward  the  muzzle,  together  with  the  need 
for  avoiding  sudden  or  great  changes  of  section  in  the  various 
forgings,  sometimes  dictates  dimensions  not  otherwise  desirable. 

2.  GUN  CONSTRUCTION. — The  1 6-inch  Breech-loading  Rifle 
(Type,  Model  1895),  completed — except  as  to  the  final  boring, 
rifling,  and  the  hoops  engaging  the  mount  —  during  the  year  1900 
by  the  Ordnance  Department,  U.  S.  A.,  at  the  Watervliet  Arsenal, 
N.  Y.,  is  not  only  the  most  powerful  gun  yet  built,  but  is  also  the 
largest  construction  ever  assembled  by  shrinkage.  The  general 
data  *  are  as  follows  : 

Weight  of  gun  126  tons  (252,000  Ibs.),  of  armor-piercing  pro- 
jectile, 2,400  Ibs.,  of  powder-charge  (smokeless),  576  Ibs.;  powder- 
pressure,  37,000  to  38,000  pounds  per  sq.  in.;  muzzle-velocity, 
2,300  ft.  per  second  ;  muzzle-energy,  88,000  ft.-tons  ;  penetration 
in  steel  at  muzzle  (De  Marre's  formula,  normal  impact),  42.3  in.  ; 
range,  20,978  miles;  height  of  trajectory,  30,51 6  ft.  (about  5^ 
miles) ;  length  of  projectile,  5  ft.  4  in. ;  cost  per  round,  powder 
and  shot,  $1,000. 

(a)  Description. — The  gun  is  shown  in  section  in  Fig.  19.  Its 
total  length  is  590.9  in.;  external  diameter  at  rear,  60  in.,  at 
muzzle,  28  in.;  length  of  main  bore,  448.5  in.,  diameter,  16  in.  ; 
rifling,  96  lands,  96  grooves ;  depth  of  groove,  0.06  in.  ;  the 

*  Ordnance  Department,  U.  S.  A.,  "Notes  on  the  Construction  of  Ordnance,"  No.  78. 


SHRINKAGE   AND    PRESSURE  JOINTS. 


37 


38  MACHINE   DESIGN. 

rifling  curve  is  a  semi-cubic  parabola,  ranging  from  one  turn  in  50 
calibers  to  one  in  25  at  the  muzzle.  The  cylindrical  part  of  the 
powder-chamber  is  90.7  in.  long,  and  18.9  in.  diameter,  and  is  con- 
nected with  the  bore  by  a  conical  slope  24  in.  long.  The  volume 
of  the  chamber  is  29,385  cu.  in.  The  recess  for  breech-block  is 
24.4  in.  long,  with  a  diameter  at  top  of  thread  of  24.86  in.  The 
breech-mechanism  is  after  the  "  Stockett  System."  The  gun  is 
built  up  of  parts,  as  follows  : 

The  tube,  566.5  in.  long,  with  a  maximum  outside  diameter  of 
29.3  in.;  two  C-hoops  shrunk  upon  the  tube  from  the  forward  end 
of  the  jacket  to  the  muzzle ;  the  jacket,  304.65  in.  long,  shrunk 
upon  rear  of  tube,  and  overhanging  the  latter  by  24.4  in.  to  form 
the  breech-recess;  the  D-koop,  144.5  m-  l°ng>  encircling  forward 
end  of  jacket  and  rear  of  (7-hoop,  and  having  two  locking 
shoulders  in  its  bore  which  engage  corresponding  projections  on 
jacket  and  £T-hoop,  thus  preventing  any  sliding  backward  of  the 
former  or  forward  of  the  latter,  from  the  shock  of  firing ;  three 
A-hoops,  A-i  covering  the  joint  between  the  Z>-hoop  and  the 
jacket,  and  A-2,  A-j,  being  shrunk  over  the  outer  surface  of  the 
latter  ;  four  B-hoops,  encircling  the  ^4-hoops. 


Weights  (Ibs.). 

Rough. 

Finished. 

Tube  with  (7-hoops. 
Jacket. 
Hoop  D. 
'      A-i. 

'         A-2. 

'      A-3. 
'    *B, 
•    *B-i,  B-2,  B-S. 

124,351 
90,058 
26,965 
19,859 
16,137 
20,163 

58,620 

100,260 
73,900 
23,900 
14,910 
15,120 
19,940 

The  tube  and  jacket  were  each  made  from  a  nickel-steel  ingot, 
not  fluid-compressed,  and  octagon  in  section.  After  removing  the 
discards,  a  longitudinal,  axial  hole  was  bored  through  the  remain- 
ing block  and  the  tube  or  jacket  was  then  forged  hollow  on  a 
mandrel  under  a  hydraulic  press.  The  completed  forging  was 
then  rough-turned,  bored,  tempered  in  oil,  and  annealed.  The 
hoops  were  made  of  fluid-compressed  steel  containing  no  nickel. 
Excepting  that  the  ingots  were  round,  the  general  process  was 
similar  to  that  for  the  tube  and  jacket.  The  hoop-metal  was  the 
harder,  i.  e.,  having  the  greater  elastic  limit  and  tensile  strength. 

*  Awaiting  decision  as  to  carriage. 


SHRINKAGE   AND    PRESSURE  JOINTS.  39 

All  forgings  were  of  sufficient  total  length  to  provide  test- metal. 
The  specimens  for  tube  and  jacket  were  0.564  in.  diameter  and  3 
in.  long.  The  average  physical  qualities  obtained  in  all  tests  are : 


Tube. 

Jacket. 

Hoops. 

Elastic  limit,  Ibs.  per  square  inch.                     5^,375 

52,250 

57,125 

Tensile  strength,  Ibs.  per  s 

quare  inch. 

84,350 

87,800 

107,050 

Elongation,  per  cent. 

20.38 

22.16 

IQ.28 

Contraction,  "      " 

41-93 

48.32 

45-52 

(£)  Shrinkage  Furnace.  —  The  furnace  used  in  expanding  the 
parts  for  assemblage  is  shown  in  Fig.  20.  It  consists  of  a 
wrought-iron  "cage"  or  frame-work  A,  surrounding  immediately 
a  cylindrical  wall  B  of  fire-brick,  the  whole  resting  upon  solid 
rock,  at  the  3O-ft.  level,  in  a  corner  of  the  shrinkage-pit  (Fig.  21). 
The  thickness  of  the  wall  is  13  in.  and  its  internal  diameter  is  8  ft. 
4  in.  A  cylindrical  muffle  C,  built  of  ^2 -in.  boiler  steel,  sur- 
rounds the  hoop  to  be  heated.  The  outer  diameter  of  the  muffle 
is  6  ft.  6  in.,  there  being,  thus,  an  annular  space,  1 1  in.  wide,  which 
forms  a  combustion-chamber  for  the  burning  gases.  The  furnace  is 
27  ft.  9  in.  high ;  its  top  is  2  ft.  3  in.  below  the  floor-level ;  it  is 
closed  by  a  removable  cover  D,  which  confines  the  steam  and 
gases ;  and  the  products  of  combustion  are  drawn  off  through  a 
flue  connecting  the  top  of  the  chamber  with  the  main  chimney. 

Fuel  oil  is  supplied  through  a  3 -in.  pipe  from  a  5,ooo-gallon 
tank  and  enters  the  furnaces  through  20  burner-openings  E,  set 
in  five  tiers  F,  of  four  burners  each.  The  burner  consists  of  an 
internal  steam-pipe  of  /^-in.  bore,  the  latter  being  reduced  at  the 
end  to  -Jg  in.  Surrounding  this  is  a  J^-'m.  oil-pipe,  the  forward 
end  of  which  is  plugged  and  a  y^ -in.  hole  drilled  therein,  opposite 
the  Y6"^n-  °Penmg  m  the  internal  pipe.  The  steam  issuing  at  high 
velocity  through  the  latter  opening,  carries  the  oil  with  it  as  a 
spray ;  and  its  oxygen,  combining  with  the  oil,  gives  an  intensely 
hot  flame.  The  burners  are  so  directed  that  the  flame  strikes  the 
muffle  at  a  tangent  approximately,  thus  giving  a  rapid  spiral  move- 
ment to  the  gases.  The  muffle  transmits  the  heat  to  the  hoop 
and  the  circulation  of  air  within  it  tends  to  make  the  temperature 
equal  at  all  points  of  the  hoop.  The  furnace-temperature  is 
governed  by  a  damper  in  the  flue,  by  the  number  of  jets  burning, 
and  by  the  amounts  of  oil  and  steam  admitted.  Each  burner  is 
surmounted  by  an  observation  opening,  closed  by  a  mica  door. 


MACHINE   DESIGN. 


Uniformity  of  heating  is  secured  by  the  tangential  direction  of  the 
gases  and  by  the  intervention  of  the  muffle,  the  latter  keeping  the 
flames  from  impinging  directly  upon  the  hoop  and  thus  causing  local 
heating  in  excess. 

(<r)  Shrinkage-Pit. — Within  the  same  excavation  which  contains 
the  shrinkage-furnace,  the  shrinkage -pit  (Fig.  21)  is  located,  the 

latter  being  60  ft.  deep  and 
cut  from  the  solid  rock. 
To  hold  the  gun  during 
the  shrinkage  processes, 
a  cast-iron  chuck  G  is 
anchored  in  the  concrete 
foundation  at  the  bottom 
of  the  pit  and  an  interme- 
diate chuck  H  is  placed  at 
the  35-ft  level.  Upon  this 
level,  also,  there  is  con- 
structed a  heavy  platform 
or  "  tipping  rest"  K,  for 
supporting  the  lower  end 
of  the  gun  while  it  is  lying 
in  an  angular  position,  after 
having  been  brought  to, 
and  partly  lowered  within, 
the  pit  by  two  cranes.  The 
platform  enables  one  of  the 
latter  to  lift  the  gun  to  a 
vertical  position  and  set  it  in 
the  chucks.  In  order  to 
handle  the  gun,  when  thus 
within  the  pit,  two  steel 

FIG   2I  plugs,  connected  by  a  rod  7 

in.  in  diameter  and  screwed 

into  each,  were  fitted  within  the  bore  of  the  tube,  the  plug  at  the 
upper  end  being  arranged  for  connection  with  the  bail  on  the  crane- 
hook.  A  steam-pump  to  free  the  pit  from  the  water  used  to  cool 
hoops  after  assembling  completes  the  equipment. 

(d}  Assembling. — In  preparation  for  the  shrinkage  of  the  jacket, 
the  tube  was  placed  in  the  pit,  muzzle-end  down,  and  water  con- 
nections were  made  for  interior  cooling  and  for  cooling  the  jacket 


SHRINKAGE   AND    PRESSURE  JOINTS.  41 

when  seated.  The  latter  was  then  heated  for  30  hours  and  its 
bore  calipered  three  times  during  that  period  to  determine  the  ex- 
pansion. Upon  removal  from  the  furnace,  it  was  measured, 
centered,  and  lowered  in  place  and  water  was  applied  at  the 
muzzle-end.  The  cooling  continued  for  nine  hours,  the  number 
of  the  encircling  "  water-rings  "  or  pipes  varying  from  four,  as  a 
maximum,  to  two  at  the  close  of  the  operation.  The  shrinkage 
of  the  C-  and  D-hoops  was  effected  in  a  similar  manner.  The 
A-hoops  were  assembled  with  the  gun  in  a  horizontal  position  in 
the  lathe.  The  hoists  of  a  crane  were  attached  to  straps  secured 
to  the  hoop  after  heating  and  the  latter  was  carried  to  the  gun, 
seated  in  place,  and  cooled  by  water  from  the  forward  end. 
During  contraction,  the  hoop  was  under  the  constant  pressure  of 
two  3O-ton  hydraulic  jacks,  one  on  each  side,  acting  in  the  hori- 
zontal plane  through  the  axis  of  the  gun.  It  is  proposed  to  effect 
the  seating  of  the  .5-hoops  in  a  similar  manner. 

(e)  Expansion,  Shrinkage,  and  Clearance. — The  expansion  of 
the  metal,  per  inch  of  diameter  for  each  degree  of  temperature, 
was  0.000007  in.  Thus,  for  an  exterior  diameter  of  hoop  of  64 
in.,  the  total  expansion  for  i  °  of  temperature  =  0.000448  in.,  and, 
for  800°,  =  0.358  in.  Measured  exterior  diameters  at  several 
points  on  the  surface  of  a  hoop,  if  uniformly  increased  by  ex- 
pansion, indicate  uniform  temperature  and  the  amount  of  expansion 
shows  the  degree  of  temperature.  Calling  the  diameter  of  the 
cold  tube  D,  that  of  the  cold  hoop  or  jacket  d,  and  the  shrinkage  ^: 

Expansion  =  0.000007  (D  —  s}=  E ; 
Shrinkage  =  D  —  d=  s  ; 
Clearance  =  E  +  (D  —  s)  —  D  ; 
Diameter  of  jacket  heated  =  E  -f  (D  —  s}. 


CHAPTER  II. 

SCREW   FASTENINGS. 

A  screw-surface  or  helicoid  is  described  by  a  right  line,  A-B, 
Fig.  22,  revolving  about  and  advancing  along  an  axis,  Y-Y,  as 
directrix,  one  extremity,  A,  of  the  line  remaining  upon  -the  axis 
and  the  angle  of  advance,  a,  between  the  latter  and  the  line  or 
generatrix  being  constant.  The  base-angle,  /?,  is  the  complement 

Y 


of  the  angle  of  advance.  In  the  screw-thread,  the  generating  line 
is  replaced  by  a  plane  figure  —  as  the  triangle,  B-E-F,  a  rec- 
tangle, or  a  trapezoid  —  maintained  always  in  an  axial  plane  and 
in  contact  with,  and  traversing  a  helical  path  upon,  the  surface  of 
a  cylinder,  as  G-H-K-L. 

42 


SCREW   FASTENINGS.  43 

The  nominal,  or  outer  diameter,  D,  of  a  screw  is  that  of  the 
outside  or  top  of  the  thread.  The  effective  diameter,  d,  is  that  of 
the  base  or  root  of  the  thread  and  of  the  cylinder  or  core  upon 
which  the  latter  is  described.  The  depth  of  the  thread  is  the  radial 

D  —  d 
distance  between  its  base  and  top,  i.  e., "£\v& pitch,  p,  is  the 

axial  distance  between  adjacent  convolutions  of  the  same  thread, 
/.  e.,  the  axial  distance  which  the  nut  traverses  during  one  revolu- 
tion. The  pitch-angle,  d,  of  any  helix  of  the  thread,  is  the  inclination 
between  that  helix  and  a  plane  perpendicular  to  the  axis  of  the 
cylinder.  While,  in  a  normal  screw,  the  pitch  of  all  helices  is  the 
same,  the  pitch-angle  of  each  depends  upon  its  diameter.  Cal- 
culations with  regard  to  stresses  within  the  thread  are  referred 
to  the  mean  thread-diameter,  d0,  (of  pitch-angle  <50),  at  which  all 
forces  are  assumed  to  be  concentrated.  This  diameter  may  be 
taken  also,  with  sufficient  accuracy,  as  that  of  the  mean  helix, 
equally  distant  from  the  helices  at  base  and  top  of  thread.  The 
projected  area  of  the  thread  is  used  in  computations  for  bearing 
pressure. 

In  addition  to  differences  in  the  forms  of  the  threads,  screws 
are  distinguished  further  as  right-  or  left-handed  and  single-  or 
multiple-threaded.  In  a  right-handed  screw,  the  thread  ascends 
contra-clockwise  from  left  to  right.  Screw-fastenings  have  usually 
a  single,  right-handed,  approximately  triangular  thread.  A  mul- 
tiple (double,  triple)  threaded  screw  is  one  in  which  the  cylinder 
is  traversed  by  two  or  more  threads,  parallel  and  similar  in  all 
respects.  Such  screws,  having  ample  bearing  surface,  are  used 
for  the  transmission  of  power. 

The  screw  and  its  nut  form,  kinematically,  a  pair ;  the  relative 
motion  of  whose  two  elements  consists  of  rotation  about  an  axis 
and  translation  along  the  latter.  If  the  material  of  the  nut  be 
relatively  inelastic,  as  metal,  the  requirement  for  motion  as  above, 
is  that  the  ratio  between  translation  and  rotation  shall  be  constant, 
i.  e.,  that  there  shall  be  uniform  pitch.  When,  however,  the  screw 
revolves  in  a  mobile  medium  or  nut,  as  water,  its  surface  may 
have  a  varying  pitch  throughout.  The  marine  propeller  is  a 
transverse  section  of  a  multiple-threaded  screw,  the  pitch  of  whose 
blade-surface  may  be  either  constant  or  expand  in  either  or  both 
of  two  ways  —  radially  outward  or  from  the  leading  to  the  follow- 
ing edge  of  the  blade. 


44 


MACHINE   DESIGN. 


ii.     Triangular  vs.  Square  Threads. 

The  form  of  the  thread  is  determined  by  the  character  of  its 
service.  The  more  important  differences  between  the  square 
thread  and  the  full  or  modified  triangular  type  lie  in  the  relative 
strengths  of  these  forms  and  the  friction  of  operation.  The  load 
in  a  bolt  is  usually  axial.  It  is  transmitted  to  the  bolt-thread  and 
supported  by  the  reaction  of  the  nut-thread.  The  load-action  and 
the  nut-reaction  must  be,  for  equilibrium,  equal.  These  mutual 
actions  are,  disregarding  friction,  normal  to  the  contact  surfaces, 
i.  e.,  to  the  threads.  Considering  friction,  the  reactions  are  di- 
verted from  the  normal  by  the  angle  of  friction,  <p. 

Fig.  23  represents  sec- 
tions of  triangular  and 
square-threaded  bolts  of 
the  same  pitch.  Let  W 
and  W^  be  the  axial 
loads  respectively,  n  the 
number  of  threads  in 

W 

each  nut.  and   w  =  — 
n 

W, 

and  wl  =  — ,  the  respec- 
tive loads  per  thread. 
Disregarding  the  small 
angle,  y,  the  lines  of  ac- 
tion, a-b  and  e-f  of  the 
pressures  due  to  the  loads  will  be  normal  to  the  respective  thread- 
surfaces.  Consider  the  threads  with  regard  to : 

1.  FRICTION.  — This  is  directly  proportional  to  the  normal  pres- 
sure upon  the  contact-surfaces.     With  the  square  thread,  the  unit- 
pressure  upon  the  nut  =  e-f  and  2. 'e-f  =  wl ;  but,  with  the  trian- 
gular form,  this  unit-pressure  =  a-b,  whose  components  are  a-c 
and  b-c.     The  latter  acts  to  burst  the  nut  while  2a-c  =  w.    Since 
a-b  ;>  a-c,  there  is,  other  things  equal,  greater  friction  with  the 
triangular  thread. 

2.  STRENGTH.  —  In  the  triangular  thread,  the  section  at  the  root 
is  the  full  length  of  the  nut,  while,  in  the  square  form,  the  sec- 
tion is  but  one  half  this  length.     Against  shearing  and  flexure 
at  the  root,   the  latter   thread  is,  therefore,   proportionately  the 
weaker. 


FIG.  23. 


SCREW   FASTENINGS.  45 

3.  NUT. — As  noted,  the  triangular  type  has  a  bursting  action 
upon  the  nut,  which  action,  disregarding  friction,  does  not  exist 
with  the  square  thread. 

In  general,  the  triangular  form  is  more  suitable  for  screw-fasten- 
ings, owing  to  its  greater  strength,  its  increased  frictional  holding 
power  which  prevents  backing  off  under  load,  and  the  finer  pitches 
permissible  by  the  full  section  at  the  base  of  the  thread.  On  the 
other  hand,  the  square  thread  is  better  adapted  for  power-trans- 
mission, since  it  has  less  friction  and  its  bursting  effect  upon  the 
nut  is  so  small  as  to  be  negligible. 

12.    Requirements  of  the  Screw-Thread. 

The  screw  is  used  as  a  detachable  fastening  in  joining  the  mem- 
bers of  a  structure  or  machine;  in  producing  pressure  or  tension,  as 
in  the  screw-jack  and  testing-machine  ;  and  for  the  transmission  of 
power  and  conversion  of  motion,  as  in  the  worm-gear  and  screw 
propeller.  Its  requirements  for  these  uses  are  : 

1.  POWER.  — This  depends  upon  the  pitch  and  form.     The  effect 
of  the  latter  upon  the  strength  and  power  of  thread  has  been  dis- 
cussed.    With  a  given  applied  force,  the  less  the  pitch,  the  greater 
the  axial  load  may  be,  since  the  pitch  fixes  the  angle  of  the  inclined 
plane  upon  which  the  load  virtually  moves. 

2.  STRENGTH.  — This  is  governed  by  the  pitch,  form  and  depth 
of  the  thread.     With  constant  load,  the  steeper  the  pitch,  the 
greater  must  be  the  applied   power  and  the  consequent  normal 
pressure  upon  the  thread.     For  the  same  load  and  nominal  diam- 
eter, the  deeper  the  thread,  the  less  its  mean  bearing-pressure  will 
be  ;  but  the  moment  of  the  load  upon  the  root  will  be  larger  and 
the  effective  diameter  of  the  bolt  to  resist  tension,  will  be  reduced. 

3.  DURABILITY. — The  most  durable  thread  is  one  whose  form 
produces  the  least  friction,  whose  depth  gives  minimum  bearing 
pressure,  and  which  is  most  accurately  fitted. 

13.     Elements  of  the  Screw-Thread. 

The  requirements  of  the  screw-thread  make  its  elements  inter- 
dependent. Consider : 

i.  EFFECTIVE  DIAMETER. — This  depends  upon  the  axial  load 
and  the  torsional  stress  produced  by  friction  between  the  threads 
in  setting  up  the  nut.  The  magnitude  of  the  latter  stress  is  gov- 


46  MACHINE   DESIGN. 

erned  by  the  applied  power,  and  that  of  the  power  by  the  axial 
load  and  pitch. 

2.  PITCH. — The  relations  between  pitch  and  diameter  in  the 
prevailing  systems  of  screw-threads  are  the  outcome  less  of  log- 
ical analysis  than  of  long  experience.      For  screw-fastenings,  the 
limit  in  one  direction  lies  in  the  fact  that,  with  an  excessively 
coarse  pitch,  the  depth  will  be  too  great  and  the  effective  diameter 
will  be  reduced  unduly.     Again,  that  component  of  the  pressure 
which  is  parallel  to  the  thread -surfaces  will  exceed  the  force  of 
friction  between  the  latter,  and,  owing  to  this  excess,  the  nut  will 
back  off.     On  the  other  hand,  with  an  unduly  small  pitch-angle, 
the  surface-friction  will  form  too  large  a  proportion  of  the  total 
work  of  setting  up  the  nut,  the  torsional  action  upon  the  bolt  will 
be  excessive,  and  the  latter  may  be  sheared.      In   general,  fine 
pitches  are  unsuitable  for  soft  metals  and  coarse  pitches  for  shal- 
low holes. 

3.  FORM.  — As  stated,  the  square  thread  is  the  form  best  adapted 
for  power-transmission.     For  large  fastenings  requiring  to  be  read- 
ily and  frequently  removed  and  which  are  strained  heavily,  but 
in  one  direction  only,  as  the  breech-block  of  a  gun,  the  trapezoidal 
thread  (Fig.  30)  is  most  suitable.     This  thread  has  the  acting  face 
normal  to  the  axis,  the  rear  face  at  an  angle  thereto,  and  combines 
the  greatest  strength  and  least  friction  attainable. 

For  screw-fastenings  in  general,  the  triangular  thread,  with 
blunt  top,  straight  sides,  and  filled-in  base-angle,  was  adopted 
through  various  considerations  with  regard  to  strength,  friction, 
durability,  ease  of  manufacture,  and  conformity  with  general  prac- 
tice. Thus,  in  strength  and  frictional  holding  power,  this  form  is 
superior ;  its  straight  sides  give  even  wear  and  maximum  bearing 
surface ;  the  angle  between  them  is  fixed,  in  the  various  systems, 
by  compromises  between  the  conditions  as  to  strength,  friction, 
bursting  action  upon  the  nut,  and  facility  of  verification  and  pro- 
duction ;  the  flat  or  rounded  top  reduces  the  liability  to  injury ; 
and  the  filling  in  of  the  reentrant  base  angle  increases  the  effec- 
tive diameter  of  the  bolt  and,  in  the  Seller's  system,  the  resilience 
of  the  latter  also. 

4.  NUT.  —  The  nut  may  yield  either  by  the  shearing   or  rup- 
ture of  its  threads  or  by  bursting  from  the  action  of  the  outward 
component  of  the  pressure  upon  the  thread.     The  latter,  both  on 
bolt  and  nut,  acts  as  a  cantilever  beam,  fixed  at  the  root  and  loaded 


SCREW   FASTENINGS.  47 

uniformly  over  the  bearing  surface.  When  worn,  the  area  of 
the  latter  is  reduced,  the  bearing  becomes  irregular,  the  load  is 
practically  concentrated,  and  the  bending  moment  at  the  root  may 
be  increased.  If  the  nut  is  of  a  metal  materially  weaker  than  that 
of  the  bolt,  its  depth  should  be  greater  than  the  normal.  In  any 
event,  this  depth  should  be  sufficient  to  give  ample  strength 
against  flexure  and  shear  at  the  root  of  the  thread,  to  provide 
sufficient  bearing  surface  to  prevent  abrasion,  and  to  afford  a  good 
hold  for  the  wrench. 

5.  MULTIPLE  THREADS.  —  In  power-transmission  screws  of  large 
pitch,  a  single  thread  will  provide  adequate  bearing  surface  only 
by  having  a  depth  so  great  as  to  give  an  unduly  small  effective 
diameter  of  bolt.  When  the  pitch  is  sufficient  to  permit  it,  the 
use  of  two  or  more  parallel  threads  of  usual  proportions  will 
secure  the  required  surface  with  a  normal  effective  diameter.  Such 
threads  are  usually  of  square  or  trapezoidal  form. 

14.     The  United  States  Standard  (Sellers)  Thread. 

It  would  be  difficult  to  overestimate  the  services  to  English- 
speaking  engineers  of  Mr.  William  Sellers  and  of  his  predecessor 
in  the  same  field,  the  late  Sir  Joseph  Whitworth,  in  the  investiga- 
tions and  efforts  which  led  to  the  wide  adoption  of  the  respective 
systems  of  screw  threads  which  bear  their  names.  The  two  sys- 
tems are  in  essentials  almost  identical.  That  of  Sellers  was  orig- 
inally presented  by  him  before,  and  recommended  by,  the  Frank- 
lin Institute  in  1864.  It  was  adopted  later,  with  trifling  modifica- 
tion, by  the  U.  S.  Navy  and  War  Departments  and  by  the  Master 
Mechanics'  and  Master  Car  Builders'  Associations  and  is  now 
known  as  the  U.  S.  Standard  System  of  Screw  Threads. 

The  thread,  as  shown  in  Fig.  24,  is  triangular  with  flat  sides  in- 
clined at  an  angle  of  60°,  the  apex  being  cut  off  and  the  base 
filled  in  to  a  radial  distance  in  each  case  of  one  eighth  the  height 
of  the  primitive  triangle  making  "flats,"/",  at  these  points  each 
one  eighth  of  the  pitch,  />,  in  length.  The  Sellers  system  provides 
dimensions  for  bolts  from  one  fourth  inch  to  six  inches  nominal 
diameter.  The  notation  and  formulae  are : 

D  =  nominal  (outside)  diameter  of  bolt,  inches  ; 

d=  effective  diam.,  ins.  =  D  —  2s  =  D  —  \.-ip  =  D ; 

3r  n 


48  MACHINE   DESIGN. 

D-d 


s 


depth  of  thread,  ins.  = —  —  p  x  0.65  ;  (31) 


p  =  pitch  of  thread,  ins.  =  0.24  VD  +  0.625  —  0.175  ;       (32) 

n  =  number  of  threads  per  inch  =  -  ; 

/=  width  of  flat  =  ^  ;  (3  3) 

H  =  depth  of  nut,  rough  =  D  ; 
h  =  depth  of  head,  rough  =  ^  dh  ; 

dn  =  short  diam.,  hex.  or  square  nut,  rough  =  ^  D  -\-  -|"  ; 
dh  =  short  diam.  of  head,  rough  =  |-  D  +  -|/r  ; 

The  equation  for  the  pitch,  as  above,  is  an  empirical  formula  con- 
structed to  cover  diameters  within  the  scope  of  the  system.  To 
avoid  impracticable  fractions,  the  number  of  threads,  as  thus  de- 
duced, is  modified  to  secure  a  convenient  aliquot  value.  Thus, 
for  a  2  -in.  bolt  : 

/  =  0.241/2  -f  0.625  —  0.175  =  0.2138  in.; 

1/0.2138  =±=  4.68  =  n  =  say,  4.5  threads  per  in. 
The  depth  of  the  thread  is  obtained  from  the  equation  : 
s  =  \p  cos  30°  =  0.65^, 

deduced  from  the  diagram,  Fig.  24.  The  formula  for  the  short 
diameter,  dn,  of  the  nut  is  empirical  and  was  derived  from  success- 
ful practice.  The  values  of  the  depths,  H  and  //,  of  the  nut  and 
head  respectively  were  based  upon  considerations  as  to  adequate 
bearing  surface,  shearing  stress,  and  provision  for  an  efficient  hold 
for  the  wrench.  The  long  diameters  of  hexagon  and  square  fig- 
ures may  be  obtained  by  multiplying  the  corresponding  short 
diameters  by  1.155  and  MH,  respectively.  The  finished  dimen- 
sions for  the  depths  and  short  diameters  are  : 

H  finished  =  Z?  — 


The  U.  S.  Navy  Department  adopted  the  Sellers  system  with 
the    single    exception   that  no   difference  was   made  in   the   size 


SCREW   FASTENINGS. 


49 


- —  J>  -J 


G-  O.  6SJO 


f-    /*- 


'  o.aeejtr. 


fnternat'L 


y. 


•  o.ejo 


MACHINE    DESIGN. 


of  finished  and  unfinished  bolt-heads  and  nuts,  in  order  that  the 
same  wrench  might  be  used  for  both.  The  size  adopted  was  that 
given  by  Sellers  for  rough  work. 

The  formula  for  "  the  exact  diameter  of  the  tap-drill  with  no 
allowance  for  clearance  is  : 

1.2990381 
n 


d=D- 


"  The  usual  allowance  (for  clearance)  above  exact  bottom  diam- 
eter is  from  0.004  f°r  /^  mcn  to  o.oio  for  2-inch  taps."  * 

TABLE  X. 
U.  S.  STANDARD  (SELLERS)  BOLTS  AND  NUTS. 


Bolt. 

Nut. 

Head. 

Nut  and 
Head. 

Diameter.                                Area. 

Threads. 

Depth. 

Depth. 

¥ 

t 

fr 

p 

w 

If' 

|f 

i 

-! 

l|l 

A 

0.185         0.049 
0.240         0.077 

0.027 
0.045 

20 

18 

0.0063 
0.0069 

I 

| 

A 

1 

0.294 

O.I  10 

0.068 

16 

0.0078 

i 

i 

tt 

A 

0-345 

0.150 

0.093 

ii 

0.0089 

? 

1 

§i 

\ 

0.400 

0.196 

0.126 

13 

0.0096 

"s 

i 

A 

0-454 

0.249 

0.162 

12 

0.0104 

ft 

I 

H 

0.507 

0.307 

0.2O2 

II 

0.0114 

i 

i 

i  ft 

j 

0.620         0.442 
0.731         0.60  1 

0.302 
0.420 

10 

9 

0.0125 
0.0139 

i 

§ 

i! 

0.838         0.785 

0.550 

8 

0.0156         i 

fl 

JA 

0-939         0.994 

0.694 

7 

0.0179         H 

it 

1.064       1        1-227 

0.893 

7 

0.0179            T¥ 

i 

2 

I-I59 
1.284 

1.485 
1.767 

1-057 
1.295 

6 
6 

0.0208            if 
0.0208            1  1 

i 

2f 

1.389 

2.074 

I.5I5 

5i 

0.0227            if 

2T95 

1.490 

2.405 

1.746 

5 

0.0250            1  1 

|¥ 

2  f 

I.6I5 

2.761 

2.051 

5 

0.0250     '       1  1 

2r| 

I.7II 

3.142 

2.302 

4 

\ 

0.0278 

2 

IT95 

3 

I.96l 

3-023 

4 

\ 

0.0278             ~2\ 

I* 

3 

2.175 

4.909 

3.7I9 

4 

0.0313            2£ 

IT! 

3 

2.425 

5-940 

4.620 

4 

0.0313            2f 

2i 

4 

3 

2.629 

7.069 

5428 

3 

\ 

0.0357    j     3 

2ft 

4 

3* 

2.879 

8.296 

6.510 

3 

] 

0.0357        3* 

2  ^ 

5 

32 

3.100 

9.621 

7.548 

Si 

0.0385        3' 

2ri 

5: 

3l 

3-3I7 

11.045 

8.641 

3 

0.0417    i     3  1 

5: 

4 

3.567            12.566 

9.963 

3 

0.0417        4          3ft 

6 

4 

3.798    !    14.186 

11.329 

2 

r 

0.0435        A        3  \ 

6 

4 

4.028 

15.904 

12.753 

0.0455    !     4*        3rV 

6 

4 

4-255 

17.721 

14.226 

0.0476        41    1   3t 

7 

5 

4.480 

19.635 

15.763 

0.0500 

5       !    3if 

7 

5 

4-73° 

21.648 

17.572 

0.0500        5£        4 

8 

5 

4-953 

23.758 

19.267 

0.0526        si-     !    4ft 

84 

I 

5-203 
5423 

25.967 
28.274 

21.262 
23.098 

0.0526        s|        4f           8f 
0.0556        6          4ft          9! 

*  "Standards  of  Length,"  G.  M.  Bond,  1887,  p.  169. 


SCREW   FASTENINGS.  51 

The  Sellers  system  was  investigated  exhaustively  by  a  Board  of 
U.  S.  Naval  Engineer  officers  in  1868.  This  Board  *  found  as  to 

i.  Pitch.  The  relations  of  pitch  and  diameter  did  not  differ 
materially  from  the  average  proportions  dictated  by  good  practice. 
2.  Form.  The  thread,  as  compared  with  that  of  ordinary  V  form, 
gave  with  equal  pitches  a  greater  effective  diameter  and  was  less 
liable  to  injury.  Further,  in  the  most  unfavorable  case — that  of 
the  one-fourth-inch  bolt — where  the  inclination  of  the  thread  and 
the  torsional  stress  are  maxima,  the  tendencies  of  the  bolt  to  yield 
to  tension  or  torsion  are,  with  clean  and  well-lubricated  surfaces, 
about  equal.  3.  Nut.  To  resist  shearing  (stripping)  of  the  thread, 
the  depth,  H  =  D,  gives  a  marked  excess  of  strength  for  perfect 
threads,  since,  for  the  latter,  but  0.357^  is  required.  With  regard 
to  bearing  surface  for  fastenings,  the  depth,  H,  provides  as  much 
or  more  than  nuts  were  given  ordinarily.  The  diameter,  dn,  was 
found  to  give  ample  security  against  bursting  action,  since,  neglect- 
ing the  resistance  of  the  thread  and  taking  the  entire  section  of 
the  bolt  as  effective,  the  required  diameter,  dn=  i^D.  4.  Head. 
The  depth,  h,  was  sufficient  to  provide  fully  against  shearing  and 
to  afford  an  efficient  hold  for  the  wrench. 

The  proportions  of  the  Sellers  system  are  given  in  Table  X. 

15.     Modifications  of  the  Sellers  System. 

Experience  with  the  proportions  of  this  system  has  resulted  in 
modifications  as  to  : 

1.  PITCH   AND    DIAMETER.  —  For  nominal  diameters   ranging 
from  2^  ins.  to  6  ins.,  equation    (32)   gives   the  corresponding 
numbers  of  threads  per  inch  as  ranging  from  4  at  2^  in.  to  2^ 
at  6  in.     These  proportions,  theoretically,  should  be  such  as  will 
give  a  bolt  equally  strong  in  all  respects.     In  naval  practice  and  in 
that  of  many  large  companies,  it  is  now  customary  to  make  the 
number  of  threads  per  inch  4  for  all  diameters  from  2  y2  in.  to  6  in., 
inclusive,  thus  increasing  materially  the  effective  diameter  of  the 
bolt.      The  proportions  of  bolts  and  nuts  now  prescribed  by  the 
Bureau  of  Steam  Engineering,  U.  S.  Navy,  are  given  in  Table  XI. 

2.  BOLT-HEADS  AND    NUTS. — The    proportions  of  nuts    and 
bolt-heads,   as  given  in  the  Sellers  system,  require  odd  sizes  of 
bar-metal,  not  usually  rolled  by  the  mills,  for  the  nuts  and  addi- 

*  "  Report  of  Board  to  Recommend  a  Standard  Gauge  for  Bolts,  Nuts,  and  Screw- 
Threads  for  U.  S.  Navy."  May,  1868. 


MACHINE   DESIGN. 


tional  upsets  in  order  to  obtain  sufficient  metal  for  the  standard 
head.  Tables  XII.  and  XIII.  give  dimensions  which  are  without 
these  disadvantages. 

3.  CIRCULAR  NUTS.  —  The  Sellers  system  gives  the  dimensions 
of  hexagonal  and  square  nuts  only.  The  former  are  lighter,  their 
long  diameter  is  less,  and,  where  the  movement  of  the  wrench  is 
restricted,  they  are  more  readily  screwed  home.  The  circular, 
grooved  nut  is  a  form  applicable  for  use  in  a  confined  space  and 
is  of  especial  value  where  very  large  sizes  are  required  as,  for  ex- 
ample, on  the  end  of  a  propeller  shaft.  The  outside  diameter  of 
the  circular  nut  is  equal  to  the  short  diameter  of  the  other  types, 

TABLE  XI. 

STANDARD   DIMENSIONS  OF  BOLTS  AND  NUTS  FOR  U.  S.  NAVY. 
(BUREAU  OF  STEAM  ENGINEERING.) 


Dia 

IB. 

Eff.  Diam. 

Threads 

Long 

Diam. 

Short 

De 

3th. 

L 

>B 

D  —  d. 

Per   Inch. 

Hex. 

Sq. 

Diam. 

Head. 

N 

, 
1 

t' 

065? 

.072 

20 

18 

if 

If 

V 

A" 

c 

- 

.081 

16 

II 

B 

1 

|| 

t 

f 

•093 

14 

if 

II 

II 

( 

J 

f 

.100 

13 

I  £ 

1 

JL 

f 

J 

1 

.108 

12 

1 

I  f 

H 

1? 

5 

k 

.118 

II 

ft 

I  £ 

iA 

n 

1 

\ 

.130 

IO 

fi 

I  | 

i  ^ 

§ 

- 

•144 

9 

fi 

2TV 

IT\ 

ft 

r 

.162 

8 

l 

2JL 

i  f 

13. 

.186 

7 

A 

2T\ 

iH 

II 

.186 

7 

T5. 

2|£ 

2 

i  " 

.217 

6 

H 

3A 

2T3^ 

133* 

.217 

6 

1 

3« 

2j 

JtV 

.236 

Si 

H 

IT9J 

i. 

.260 
.260 

5 
5 

3^ 
4A 

2|" 

2r? 

I* 

i 

.289 

31! 

4H 

3* 

IT9jJ 

r 

.289 

4? 

4A 

4rw 

3* 

I  f 

I 

. 

.325 

4 

4|f 

5H 

3* 

IT! 

; 

| 

4 

6 

4 

2  i 

i 

3 

4 

sH 

6H 

4 

2f\ 

3 

3 

4 

5tt 

7A 

5 

2  5 

3 

r 

3 

4 

6^ 

7H 

5 

2T5 

3 

; 

3 

4 

8i 

5 

3 

f 

4 

4 

7A 

SH 

6 

4 

4- 

; 

4 

9r3i; 

6 

3i 

4 

| 

4 

7H 

9lt 

6 

3A 

4 

4 

4 

8f 

10  i 

7 

31 

4 

5 

4 

8$ 

lOff 

71 

3« 

5 

1 

4 

4 

9l 
9« 

"A 

S? 

8 
8} 

4A 

5 
5 

5 
6 

4 
4 

I0?f 
io{j 

I2ff 

y 

4| 

6 

E 

SCREW   FASTENINGS. 


53 


plus  twice  the  depth  of  the  groove.  In  large  sizes,  this  diameter 
is  less  than  the  long  diameter  of  the  hexagonal  form.  Good  pro- 
portions for  circular  nuts  are  given  in  Table  XIV. 


TABLE  XII. 

MANUFACTURERS'  STANDARD  DIMENSIONS  OF  BOLT  HEADS. 
(AMERICAN  IRON  AND  STEEL  MANUFACTURING  COMPANY.) 


Diameter,  Bolt. 

Square  and  Hexagon 
Heads, 

Diameter,  Bolt. 

Square  and  He; 
Heads, 

cagon 

Width  and  Thickness. 

Width  and  Thickness. 

A 

i  XA 
MX  i 
A  X  A 

I 
I] 

I 

1 

I*   X     i 
IUX 

IT  X  i 

F 

i 

MX  f 
IXA 

fix  i 
8x§ 

III 

• 

i 

iiX  f 

2}fX     1 

• 

i 

iAX  f 

2 

3      Xii 

TABLE  XIII. 

MANUFACTURERS'  STANDARD  DIMENSIONS  OF  HOT-PRESSED  NUTS. 
(AMERICAN  IRON  AND  STEEL  MANUFACTURING  COMPANY.) 


SQUARE. 


HEXAGON. 


A 


Short  Dia.      Thickness.          Hole.  Size,  Bolt 


54 


MACHINE    DESIGN. 


TABLE  XIV. 

ROUND  SLOTTED  NUTS. 

(NEWPORT  NEWS  SHIPBUILDING  AND  DRY  DOCK  COMPANY.) 


Diameter  of 
Bolt. 


Diameter  of 
Bolt. 


r 


16.     The  Sharp  "V"  Thread. 

This  thread  has  been  superseded  very  largely  in  the  United 
States  by  that  of  Sellers.  As  shown  in  Fig.  25,  the  sides  are  in- 
clined to  each  other  at  an  angle  of  60°  and  have  a  sharp  apex  and 
base.  A  section  of  the  thread  forms,  therefore,  an  equilateral  tri- 
angle, each  side  of  which  is  equal  to  the  pitch  of  the  screw. 
Using  previous  notation  : 

s=p  cos  30°  =  0.866/; 

d=  D—  2s  =  D—  1.732/5 


The  pitch  is  usually  that  of  the  Sellers  system. 


SCREW   FASTENINGS. 


55 


17.    The  Whitworth  System  of  Screw-Threads. 

In  1841  the  late  Sir  Joseph  Whitworth  brought  forward,  in  a 
communication  to  the  Institution  of  Civil  Engineers,  the  system 
of  screw-threads  which  bears  his  name.  This  system,  modified 
slightly  in  1857  and  1861,  has  met  universal  adoption  in  Great 
Britain  and  extended  use  upon  the  continent  of  Europe.  The 
range  of  diameters  was  originally,  as  in  the  Sellers  system,  from 
one  quarter  inch  to  six  inches. 

TABLE  XV. 
WHITWORTH  SYSTEM.     BOLTS  AND  NUTS. 


Bolt. 

Hexagon. 

Diameter. 

Area. 

Pitch. 

Threads. 

Head. 

Nut  and  Head. 

Nominal, 
D. 

Effective, 
d. 

Effective. 

P- 

Per  Inch, 

Depth, 

Short  Diam., 
dn  and  </A. 

\ 

• 

0.186 

0.0272 

0.0500 

20 

0.2187 

0.525 

i 

I 

0.241 

0.0456 

0.0555 

18 

0.2734 

0.6o  I 

i 

0.295 

0.0683 

0.0625 

16 

0.3281 

0.709 

T 

V 

0.346 

0.0940 

0.0714 

14 

0.3828 

0.820 

j 

• 

0-393 

O.I2I3 

0.0833 

12 

0-4375 

0.920 

- 

• 

0.508                0.2035 

0.0909 

II 

0.5468 

1.  100 

0.622                0.3038 

0.1000 

10 

0.6562 

1.300 

1 

r 

0.732 

0.4219 

O.IIIO 

9 

0.7656 

1.480 

0.840 

0.5542 

0.1250 

8 

0.8750 

1.670 

0.942 

0.6969 

0.1428 

7 

0.9843 

1.  860 

1.067 

0.8942 

0.1428 

7 

1.0937 

2.050 

1.161 

1-0597 

0.1666 

6 

I.203I 

2.210 

1.286 

1.3009 

0.1666 

6 

1.3125 

2.410 

1.368 

I.47I9 

O.2000 

5 

I.4I28                2.570 

Ij 

1.494 

1-7530 

0.2000 

5 

I-53I2                2.750 

I: 

1-590 

I.9855 

0.2222 

4* 

1.6406 

3-020 

2 

I.7I5 

2.3101 

0.2222 

44 

1.7500 

3.I50 

2; 

• 

1.930 

2.9255 

0.2500 

4 

1.9687 

3-540 

2 

2.180 

3.7325 

O.250O 

4 

2.1875 

3.890 

2: 

2.384 

44637 

0.2857 

3 

2.4062 

4.180 

3 

2.634 

5-4490 

0.2857 

3 

2.6250 

4-530 

s 

1 

2.856 
3-105 
3-320 

6.4063 
7.5769 
8.6726 

0.3077 
0.3077 
0-3333 

3 
3 
3 

2.8256 
3.0624 
3.2812 

4.850 
5.I70 
5-550 

4 

3-573 

10.0270 

0-3333 

3 

3.5000 

5-950 

4^ 

• 

3.804 

11.3710 

0.3478 

3.7046 

6.370 

4^ 

• 

4-054 

12.9140 

0.3478 

3^9374 

6.820 

• 

4.284 

I44HO 

0.3636 

4-1562 

7-300 

5 

4-534 

16.1460 

0.3636 

4-3750 

7.800 

11 

• 

4.762 

5-012 

17.8100 
19.7290 

0.3809 
0.3809 

4.5936 
4.8124 

8.350 
8.850 

si 

• 

5.240 

21.5490 

0.4000 

5-0312 

9-450 

6 

5-487 

23.6540 

0.4000 

5-2500 

IO.OOO 

As  shown  in   Fig.  26,  the  thread  is   triangular  in  section,  the 
angle    between    the    sides    being    55°.     The    primitive    triangle 


$6  MACHINE   DESIGN. 

is  rounded  off  at  the  top  and  bottom  by  an  amount  equal,  in 
each  case,  to  one  sixth  of  its  height,  making  the  depth  of  the 
thread  two  thirds  of  the  altitude.  The  relation  between  di- 
ameter and  pitch,  the  angle  of  the  sides,  and  the  depth  of  the 
thread  were  determined  by  taking  the  mean  of  the  variations  in 
these  respects  of  a  large  collection  of  screw-bolts  gathered  from 
the  principal  machine-shops  throughout  England.  The  one  quar- 
ter inch,  one  half  inch,  one  inch,  and  one  and  one  half  inch  bolts 
were  examined  particularly  and  taken  as  the  fixed  points  of  a 
scale  by  which  intermediate  sizes  were  regulated,  deviation  from 
the  exact  average  being  made  only  to  avoid  small  fractional  parts 
in  the  number  of  threads  per  inch.  The  formulae  are  : 

s  =  y^p  -i-  tan  27°  30'=  0.64  /  ; 
d=D—2s=D— 


p  =  —  =  0.08  D  +  0.04  approximately  ; 
r  =  radius  of  rounding  =  o.  I373/. 

The  dimensions   of  the   system   are   given   in   Table   XV.      The 
depth  of  the  nut  is  equal  to  the  nominal  diameter  of  the  bolt. 

18.     The  Sharp  V,  Sellers,  and  Whitworth  Threads. 
Consider  bolts  of  the  same  nominal  diameter  in  these  systems 
with  regard  to  : 
.  i.  TENSILE  STRENGTH.  —  The  effective  diameters  are  : 

V  Thread,    d=D—  1.  732/1 
Sellers,          </=  D  —  1.3/5 
Whitworth,  d=  D  —  I.28/. 

2.  STRIPPING  OF  THREAD.  —  The  section,  at  base  of  thread,  to 
resist  shear  in  : 

V  and  Whitworth  Threads  =  /  ; 
Sellers  Threads  =  O.875/. 

3.  BEARING  SURFACE.  —  This  is  a  maximum  in  the  V  thread 
with  its  straight  sides  from  apex  to  root  and  a  minimum  in  the 
Whitworth  form    owing    to    the    rounding.     The   Sellers  thread 
holds  an  intermediate  place. 


SCREW    FASTENINGS.  57 

4.  FRICTION. — The  normal  pressure  and,  therefore,  the  friction 
are  less  in  the  Whitworth  thread  than  in  the  other  types,  owing  to 
the  smaller  angle  of  the  sides. 

5.  RESILIENCE. — The  section  of  least  diameter  is  but  a  line  in 
the  V  thread  and  is  a  flat,  \p  in  length,  in  the  Sellers  system. 
The  rounded  base  gives  the  Whitworth  form  an  intermediate  posi- 
tion.    While  the   Sellers   type    seems  thus  to  be   superior,   the 
sudden  change  in  section  at  the  bottom  of  its  thread  is  a  source 
of  weakness. 

6.  DURABILITY.  —  The  sharp  tops   of  the  V  thread  are  very 
liable  to  injury.     In  this  and  the  Sellers  form,  the  normal  pressure 
is  uniform  over  the  entire  surface,  while,  in  the  Whitworth  thread, 
it  is  uniform  upon  the  sides  and  varying  and  greater  over  the 
curved  surfaces.     The  wear  of  the  Sellers  type  will  be,  therefore, 
less  than  that  of  the  Whitworth. 

7.  REPRODUCTION. — The  60°   angle  can  be  reproduced  and 
verified  more  readily  than  one  of  55°.     The  curves  in  the  Whit- 
worth form  vary  in  radius  with  the  pitch  and  cannot  be  made  with 
the  same  degree  of  precision  as  the  flats  of  the  Sellers  system. 
The  taps  and  dies  used  in  the  making  of  the  V  thread  soon  lose 
their  fine  cutting  edges,  thus  causing  constant  variations  in  fitting. 

19.     French  Standard  Screw-Thread. 

(Sy steme  Unifie  Frangais^ 

To  the  Societe  d' Encouragement  pour  r  Industrie  Nationale  is 
due  the  credit  for  the  adoption  of  a  standard  thread  in  France. 
The  thread  form  is  practically  that  of  Sellers  based  on  metric 
units.  The  section  is  an  equilateral  triangle  whose  base  is  equal 
to  the  pitch,  the  top  of  the  triangle  being  cut  off  and  the  root  of 
the  thread  filled  in  to  form  flats,  situated  one  eighth  the  height  of 
the  triangle  from  its  apex  and  base  respectively.  As  in  the 

Sellers  system  : 

Angle  =  60°  ; 

Depth  s  =  0.65  /  ; 

Width  of  flat,  f  =-0. 
o 

The  proportions  of  the  system  are  given,  in  millimetres,  in  Table 
XVI.  It  has  been  extended  to  a  nominal  diameter  of  148  mm. 
(5.82  in.)  and  a  pitch  of  10.5  mm.  (0.4133  in.).  At  nominal 


MACHINE    DESIGN. 


diameters  of  80,  96,  106,  1 16,  126,  136  and  148  mm.,  the  pitches, 
respectively,  are:  7,  8,  8.5,  9,  9.5,  10,  10.5  mm.  The  standard 
screws  adopted  by  the  French  Navy  include  the  extended  series 
as  above  with  certain  others  intercalated  to. meet  the  requirements 
of  the  service. 

TABLE  XVI. 
FRENCH  STANDARD  SCREW-THREADS. 


Diameter. 

Thread. 

Pitch. 

Nominal,* 
D. 

Effective, 
d. 

Depth, 
s. 

/• 

mm. 

mm. 

mm. 

mm. 

6 

4.70 

0.650 

I.O 

10 

8.50 

0-975 

1-5 

14 

11.40 

1.300 

2.0 

18 

14-75 

1.625 

2-5 

24 

20.  10 

1-950 

3-0 

30 

2545 

2.275 

3-5 

36 

30.80 

2.600 

4.0 

42 

36.15 

2.925 

4-5 

48 

41.50 

3.250 

5-0 

56 

48.85 

3-575 

5-5 

64 

56.20 

3.900 

6.0 

72 

63.55 

4.225 

6-5 

80 

70.90 

4-550 

7.0 

20.     International  Standard  Screw-Thread. 

(Systeme  Internationale,  S.  /.) 

This  system  was  adopted  by  the  Congres  International  pour 
r  Unification  des  Filetages,  held  at  Zurich,  October  3-4,  1898.  Its 
proportions  differ  from  those  of  the  French  Standard  only  in  the 
pitches  of  the  screws  of  8,9,  12  and  1 3  mm.  diameter,  and  in  the 
insertion  in  the  series  of  the  odd  numbered  diameters  27,  33,  39, 
45  mm.,  which  were  not  included  in  the  French  system. 

The  rules  formulated  by  the  Congress  apply  only  to  screw- 
bolts  of  a  nominal  diameter  of  6  mm.  and  upward.  The  form  of 
the  thread  is  practically  that  of  the  Sellers  system,  excepting  that 
a  serious  defect  in  the  latter  is  avoided  by  providing  clearance  at 
the  bottom  of  the  thread.  This  clearance  must  not  exceed  one 
sixteenth  the  height  of  the  primitive  triangle.  The  top  of  the 
thread  is  flat  in  order  to  facilitate  production  and  to  reduce  the 
liability  to  injury.  The  shape  of  the  bottom  may  be  flat  or 
rounded,  the  latter  being  recommended  to  avoid  reentrant  angles 
which  aid  rupture.  The  dimensions  prescribed  by  the  Congress 

*  Dimensions  given  only  for  bolts  at  which  change  of  pitch  occurs. 


SCREW   FASTENINGS. 


59 


are  given  in  Table  XVII.  The  pitch  of  any  size  intercalated  be- 
tween those  of  standard  diameters  is  to  be  the  same  as  that  of  the 
next  smaller  diameter.  The  thread,  with  the  full  clearance  and 
curved  bottom  recommended,  is  shown  in  Fig.  27.  The  formulae 
are  : 

Altitude,  a,  primitive  triangle  =  O.866/  ; 

d=  D  —  2  x       &  =  D  — 


D-d 
s  (maximum)  =  --  =  0.703  5/  ; 

/  =  width  of  flat  =  ^  ; 


Clearance,  C  (max.)  =  — . 

TABLE  XVII. 

INTERNATIONAL  STANDARD  SCREW-THREADS.* 


Nominal 
Diameter, 
D. 

Pitch, 

/• 

Nominal 
Diameter, 
D. 

Pitch, 

P- 

Nominal 
Diameter, 
D. 

Pitch, 

P- 

mm. 

mm. 

mm. 

mm. 

mm. 

mm. 

6 

.00 

20 

2-5 

48 

5-o 

7 

.00 

22 

2-5 

52 

5-0 

8 

•25 

24 

3-0 

56 

5-5 

9 

10 

•25 

•50 

27 
30 

3-o 
3-5 

60 
64 

ii 

ii 

•50 

33 

3-5 

68 

6.0 

12 

1-75 

36 

4.0 

72 

6.5 

14 

2.00 

39 

4.0 

76 

6-5 

16 

2.00 

42 

4-5 

80 

7-0 

18 

2.50 

45 

4-5 

21.     The  British  Association  Standard  Thread. 

This  thread  was  taken,  with  a  slight  modification,  directly  from 
the  Swiss  system  of  Professor  Thury  whose  work,  for  the  small 
screws  used  in  watches  and  scientific  instruments,  was  similar  to 
that  of  Sellers  and  Whitworth  for  screw-bolts.  Thury's  investi- 
gation was  undertaken  in  1876  at  the  instance  of  the  Geneva 
Society  of  Arts.  His  system,  like  those  which  preceded  it,  was 
formulated  from  data  obtained  by  measuring  the  dimensions  of 
many  screws  accepted  as  well  proportioned.  The  form  of  the 


*  Bulletin  Soc.  d'Encour.,  March,  1899. 


6o 


MACHINE   DESIGN. 


British  Association  thread  is  shown  in   Fig.  28.     It  is  similar  to 
that  of  Whitworth.     The  angle  is  47.5°.     The  formulae  are  : 

P  =  °-9"  5 


o.6p  ; 


In  these  equations  the  quantities  are  expressed  in  millimetres. 
For  screws  characterized  as  No.  o,  No.  I,  No.  2,  etc.,  the  index 
n  has  the  values  o,  1,2,  etc.,  respectively.  The  equation  for  / 
gives  thus  a  gradually  decreasing  series,  each  pitch  being  0.9  of 
its  predecessor.  The  values  of  the  pitches  thus  obtained,  substi- 
tuted in  the  equation  for  D,  give  the  corresponding  diameters  in 
millimetres,  two  significant  figures  only  being  taken.  Table  XVIII. 
gives  the  proportions  of  this  system. 

TABLE  XVIII. 
BRITISH  ASSOCIATION  STANDARD  THREAD. 


N, 

Exact  Dimensions, 
Millimetres. 

Approximate  Dimensions, 
Inches. 

Diameter, 

Nominal, 
D. 

Pitch, 
P- 

Diameter, 

Nominal, 
D. 

Pitch, 

p. 

Threads 
Prr  Inch, 
n 

0 

6.00 

1.  00 

0.236 

0.0394 

254 

I 

5-30 

0.90 

0.209 

0.0354 

28.2 

2 

4.70 

0.81 

0.185 

0.0319 

31-4 

3 

4.10 

°-73 

0.161 

0.0287 

34-8 

4 

3-6o 

0.66 

0.142 

0.0260 

38.5 

5 

3.20 

0-59 

0.126 

0.0232 

43-0 

6 

2.80 

0-53 

O.I  10 

0.0209 

47-9 

7 

2.50 

0.48 

0.098 

0.0189 

52.9 

8 

2.20 

0-43 

0.086 

0.0169 

59-i 

9 

1.90 

0-39 

0.075 

0.0154 

65.1 

10 

1.70 

0-35 

0.067 

0.0138 

72.6 

ii 

1.50 

0.31 

0.059 

0.0122 

81.9 

12 

1.30 

0.28 

0.051 

O.OIIO 

90.7 

13 

1.20 

0.25 

0.044 

0.0098 

IOI.O 

M 

1.  00 

0.23 

0.039 

0.0091 

1  1  0.0 

J5 

0.90 

0.21 

°-°35 

0.0083 

I2I.O 

16 

0.79 

0.19 

0.031 

0.0075 

134.0 

17 

0.70 

0.17 

0.027 

0.0067 

149.0 

18 

0.62 

0.15 

0.024 

0.0059 

169.0 

19 

0.54 

0.14 

0.021 

0.0055 

181.0 

20 

0.48 

O.I2 

0.019 

0.0047 

212.0 

21 

0.42 

O.I  I 

0.017 

0.0043 

231.0 

22 

0-37 

0.098 

0.015 

0.0039 

259.0 

23 

o-33 

0.089 

0.013 

0.0035 

285.0 

24 

0.29 

0.080 

o.on               0.0031 

317.0 

25 

0.25 

0.072 

o.oio               0.0028 

353-0 

SCREW    FASTENINGS. 


61 


In  1900,  a  committee  of  the  British  Association,  appointed  to 
consider  modifications  in  this  thread,  recommended,  as  to  the 
screws  and  nuts  from  No.  o  to  No.  1 1  inclusive,  that  the  exist- 
ing proportions  remain  unchanged,  excepting  that  the  top  and  bot- 
tom of  the  thread  be  made  cylindrical,  showing  "  flats  "  in  section  ; 
and  that,  to  provide  clearance,  the  depth  of  the  thread  be  increased 
by  one  tenth  of  the  pitch,  thus  reducing  the  effective  diameter  by 
one  fifth  the  pitch.  Thus,  for  screw  No.  o,  the  nominal  and 
effective  diameter,  as  modified,  would  be  6  and  4.6  millimetres 
respectively,  while  the  corresponding  diameters  of  the  nut  thus 
modified  would  be  6.2  and  4.8  mm. 


22.     The  Square  Thread. 

The  relative  advantages  and  disadvantages  of  this  form  of  thread 
have  been  discussed  in  §n.  It  is  used  for  the  transmission  of 
power  as  in  screw-jacks,  the  leading  screw  of  lathes,  etc.  It  is 
more  costly  than  the  triangular  thread  since  it  must  be  cut  in  the 
lathe.  The  proportions  have  not  been  standardized.  The  practice 
of  two  prominent  companies  is  given  in  Tables  XIX.  and  XX. 
The  corners  of  the  thread  are  slightly  rounded  and  occasionally 
a  small  angle  is  given  its  sides,  although  the  thread-form  is  prac- 
tically square. 

TABLE  XIX. 

STANDARD  SQUARE  THREADS. 

(WILLIAM   SELLERS  &  COMPANY.) 


Nominal 
Diam., 
D. 

Threads 
Per  In., 

Effective 
Diam., 
d. 

Nominal 
Diam., 
D. 

Threads 
Per  In., 
n. 

Effective 
Diam., 
d. 

\" 

10 

.1625" 

if 

3 

1.0834" 

A 

9 

•2153 

if 

3 

1.2084 

A 

7 

.2658 
.3125 

l| 

! 

1.307 

1.4 

A 

? 

.3656 
.4167 

2 

\ 

1.525 

1.612 

A 

51 

5 

.466 
•512 

3 

2 
2 

1.862 
2.0626 

i 

5 
4| 
4| 

4 

ill 

.6806 

.7188 

2| 

i 

2 

I- 
I 
I 

[' 

2.3126 
2-5 
2-75 
2.962 

i 

4 

.7813 

3! 

I 

3.168 

«| 

3i 

.875                    4" 

I 

34l8 

1} 

3^ 

I                   ! 

62 


MACHINE   DESIGN. 


TABLE  XX. 

STANDARD  SQUARE  THREADS. 
(NEWPORT  NEWS  SHIPBUILDING  AND  DRY  DOCK  Co.) 


°s 


Diar 
Nomii 

neter, 
lal,  D. 

Diameter, 
Effective,  d. 

Area,  Effective, 
irar*-^4. 

Threads  per  In., 

Nut,  Depth, 
H. 

• 

// 

0-3333" 

0.0870 

6 

/' 

i 

0.4250 

0.1418 

5 

0.5500 

0.2376 

5 

[ 

0.6530 

0-3349 

4-5 

0.7500 

0.4418 

4 

0.8750 

0.6013 

4 

| 

0.9640 

0.7300 

3-5 

| 

I.O900 

0.9331 

3-5 

2 

1.1670 

1.0700 

3 

2} 

1.2900 

1.3070 

3 

2| 

I.4I70 

1-5770 

3 

2| 

1-4750 

1.7090 

2-5 

4 

1.  600O 

2.0106 

2-5 

3 

r 

1.8500 

2.6880 

2-5 

3l 

1 

2.0000 

3.I4I6 

2 

3f 

" 

< 

2.2500 

3.9760 

2 

4| 

3 

2.5000 

4.9087 

2 

42 

23.     The  |-V  Screw-Thread. 

This  thread  is  a  modification  of  the  square  and  triangular  forms 
designed  to  combine  some  of  the  advantages  of  both  types.  The 
sides  are  inclined  at  a  moderate  angle  and  there  are  wide  flats  at 
the  top  and  bottom.  As  compared  with  the  square  thread,  the 
various  |-V  forms  are  stronger,  being  relatively  wider  at  the  root; 
they  can  be  cut  with  a  die,  which  is  not  possible  with  the  square 
thread ;  the  fit  in  the  nut  can  be  made  closer ;  the  angularity  of 
the  sides  facilitates  the  engagement  and  disengagement  of  the 
divided  nuts  used  with  such  screws  in  the  lathe  and  permits  also 
the  wear  of  the  thread  to  be  taken  up  by  closing  the  nut ;  and 
finally  the  thread  is  cleaned  more  readily.  These  advantages  are 
obtained  without  an  excessive  increase  in  friction.  It  is  difficult, 
however,  to  keep  the  cutting  tools  to  the  exact  angle  of  the  thread. 


SCREW   FASTENINGS. 


i.  SELLERS. — Table  XXI.  gives  the  dimensions  of  the  Sellers 
thread  of  this  type.     The  formulas  are  : 

Angle  =  15°  on  side ; 
Nominal  diameter  =  D. 

TABLE  XXI. 

J-V  SCREW-THREAD. 
(WILLIAM  SELLERS  AND  COMPANY.) 


vT* 


Diam. 

Nominal, 
D. 

Pitch, 

Threads, 
No.  Per  In. 

Depth  of 
Thread, 

Width 
of  Flat  at 
Root, 
A. 

Width 
of  Flat  at 
Top, 

Angle  of  Thread 
for  Tools. 

1 

A 

10 

.0438 

.038 

.0385 

7°    15'    22" 

1 

i 

8 

.0548 

•0475 

.0481 

6      3     24 

i 

6 

\  ' 

.0674 

•0585 

.0592 

5     35     37 

T95 

6 

.0731 

.0641 

5     23     26 

| 

5 

r 

.0797 

.0691 

.07 

5     17     28 

ii 

5 

.0877 

.076 

.077 

5     17     25 

f 

5 

.0877 

.076 

.077 

4    5i       6 

if 

4^ 

r 

.0974 

.0844 

.0855 

4    58    32 

I 

4 

f 

.0974 

.0844 

.0855 

4    37     18 

\\ 

4 

.1096 

•095 

.0962 

4    5i       6 

4 

.1096 

.095 

.0962 

4    33      o 

\ 

3 

r 

•1253 

.1086 

.11 

4    37     18 

3! 

• 

•1253 

.1086 

.11 

4      9    40 

1 

i 

3 

.1461 

.1266 

.1283 

4     24    45 

| 

I 

3 

.1461 

.1266 

.1283 

4      2     46 

T4T 

1 

•1594 

.1382 

.14 

4      4     33 

f 

f 

1 

• 

•1754 

.152 

.154 

4      9    41 

|. 

i 

• 

•1754 

.152 

.154 

3     53       5 

: 

• 

.1948 

.1688 

.171 

4       2     46 

i 

• 

; 

• 

.1948 

.1688 

.171 

3     35     52 

\ 

.2192 

•19 

.1924 

3     38    33 

f 

.2192 

•19 

.1924 

3     18     44 

3 

.2505 

.2172 

.22 

3     28     ii 

3| 

.2505 

.2172 

.22 

3     12     ii 

.2698 

.234 

.2368 

3     12     ii'' 

3f 

1 

.2923 

.2532 

.2566 

3     14     20 

4 

2 

.2923 

•2532 

.2566 

3         2       12 

4i 

H 

T 

s 

•3049 

.2643 

.268 

2     58    57 

4$ 

4f 

f 

T; 

, 

.3188 
•3340 

.2764 
•2895 

.28 
•2933 

2      56      41 
2      55       22 

5 

•3507 

.304 

.308 

2    55     56 

5i 

1 

.3507 

.304 

-308 

2      46      36 

64 


MACHINE   DESIGN. 


Pitch,  /  =  0.48  V D  -f  0.625  —  0.35  ; 

Depth,  s  =  0.43  84/5 

Flat  at  root,  A  =  0.38/5 

Flat  at  top,  B  =  0.385/5 

Clearance  =  o.oip. 

2.  NEWPORT  NEWS  SHIPBUILDING  AND  DRY  DOCK  COMPANY.  — > 
The  proportions  of  this  thread  are  given  in  Table  XXII. 

TABLE  XXII. 

STANDARD   BASTARD  SCREW-THREADS. 
(NEWPORT  NEWS  SHIPBUILDING  AND  DRY  DOCK  COMPANY.) 


Diameter, 
Nominal, 
D. 

Diameter, 
Effective, 
d. 

Area, 
Effective, 
ltd*  -r-  4. 

Threads 
Per  In., 
ft. 

Width 
of   Flat, 

Nut, 
Depth, 

I// 

0-3333" 

0.0870 

6 

0.0420 

K 

| 

0.4250 

O.I4I8 

5 

0.0500 

i 

I 

0.5500 

0.2376 

5 

0.0500 

| 

0.6530 

0-3349 

4-5 

0.0560 

0.7500 

0.4418 

4 

0.0625 

0.8750 

0.6013 

4 

0.0625 

0.9640 

0.7300 

3-5 

0.0714 

1.0900 

3-5 

0.0714 

If 

1.1670 

1.0700 

3 

0.0833 

2 

1.2900 

1.3070 

3 

0.0833 

2\ 

I.4I70 

1-5770 

3 

0.0833 

2f 

1.4750 

1.7090 

2-5 

O.IOOO 

22 

1.  6000 

2.0106 

2.5 

O.IOOO 

2| 

L 

1.8500 

2.6880 

2-5 

O.IOOO 

3 

\ 

2.0000 

3.1416 

2 

0.1250 

3} 

| 

2.2500 

3.9760 

2                            0.1250 

3f 

3 

2.5000 

4.9087 

2 

0.1250 

4 

3.  ACME  STANDARD  (29°)  THREAD. — This  form  has  the  same 
depth  as  the  similar  square  thread  and  its  sides  are  at  the  same 
inclination  as  is  now  adopted  generally  in  cutting  worm  gears. 
The  formulae  are  : 

Angle  of  sides  =  14.5°  =  29°  included  angle  ; 


SCREW   FASTENINGS. 
Number  of  threads  per  inch  =  n  ; 
Width  of  flat  at  top,  B  =  °'37°7  ; 

Depth  of  thread,  s  = h  o.oi  ; 

2n 

Nominal  diameter  =  D  ; 

Effective  diameter  =  D  —  i  —  +  0.02  J. 

TABLE  XXIII. 
ACME  STANDARD  (29°)  SCREW-THREAD. 

k-. 

A        « <?* 


No.  ofThds. 
per  in.  Linear, 

Depth 
of  Thread, 

Width  at  Top 
of  Thread, 

Width  at  Bottom 
of  Thread, 
A. 

Space  at 
Top  of  Thread, 

Thickness  at 
Root  of  Thread, 
D. 

I 

.5100 

.3707 

.3655 

.6293 

.6345 

ij 

.3850 

.2780 

.2728 

•4720 

.4772 

2 

.2600 

.1853 

.l8oi 

.3147 

•3199 

3 

.1767 

•1235 

.1183 

.2098 

.2150 

4 

.1350 

.0927 

.0875 

•1573 

.1625 

5 

.1100 

.0741 

.0689 

•1259 

.1311 

6 

.0933 

.0618 

.0566 

.1049 

.nor 

7 

.0814 

.0529 

.0478 

.0899 

•0951 

8 

.0725 

.0463 

.0411 

.0787 

.0839 

9 

.0655 

.0413 

.0361 

.0699 

•0751 

10 

.0600 

.0371 

.0319 

.0629 

.0681 

24.     Special  Threads. 

1.  THE  KNUCKLE  THREAD,  Fig.  29,  may  be  considered  as  formed 
from  the  square  type  by  rounding  the  top  and  root  of  the  latter 
in  curves  which  unite.     The  curvature  increases  the  strength  and 
friction  of  the  thread  and  reduces  its  liability  to  injury  in  service. 
Its  advantage  lies  solely  in  its  fitness  for  rough  usage. 

2.  THE  BUTTRESS  THREAD,  Fig.  30,  is  a  trapezoidal  form  suit- 
able for  producing  pressure  in  one  direction  only.     The  driving 


66 


MACHINE    DESIGN. 


side  is  normal  to  the  axis  of  the  screw  as  in  the  square  thread 
the  angle  between  the  sides  is  usually  45°  ;  and  the  width  of 
the  flat  at  top  and  bottom  is  one  eighth  of  the  pitch.  For  maxi- 


FIG.  29. 


FIG.  30. 


mum  effort  in  one  direction,  the  thread  has  the  greatest  strength 
and  least  friction  attainable. 

3.  MODIFIED  BUTTRESS  THREAD.  — This  thread  meets  extended 
and  important  use  in  the  breech-blocks  of  modern  ordnance  and 
also  in  securing  armor-plate  to  the  hulls  of  war  vessels.  The 
profile  of  armor-threads  as  used  by  the  U.  S.  Navy,  is  shown  in 
Fig.  31,  the  proportions  of  various  sizes  being  given  in  Table 


I— 


— * 


XXIV.*  One  side  of  the  thread  makes  an  angle  of  I  5°  with  the 
normal  to  the  axis  of  the  bolt,  the  similar  inclination  of  the  other 
side  is  45°,  and  the  top  and  root  are  rounded  with  ample  curves. 

TABLE  XXIV. 

PROPORTIONS  OF  BOLTS   FOR  SIDE,    DIAGONAL,  AND  BELT-ARMOR,  U.  S.  NAVY. 


Outboard  End. 

Inboard  End. 

Thread. 

Armor, 
Thickness. 

Diameter, 

D.    ' 

Diameter, 
Effective, 
d. 

Diameter, 
Nominal, 
A- 

Diameter, 
Effective, 
</,. 

Depth, 
s. 

Pitch, 
P- 

Radius  of 
r. 

2.o8o" 
2.68o 
3.200 
3.680 
4.2l6 

i.8o// 

2.40 

2.88 
3.36 
3-84 

1.  780" 
2.28o 
2.720 
3.120 
3.576 

i.  So" 

2.00 
2.40 
2.80 
3.20 

0.1414" 
0.1414 
0.1604 
0.1604 
0.1885 

\ 

0.030" 
0.030 
0.035 
0.035 
0.040 

to    5"  inc. 
6"    9     " 
10  "13     " 
I4"i7    " 

l8"2I      " 

*  "  Report  of  Chief  of  Bureau  of  Construction  and  Repair,  U.  S.  Navy,"  1896. 


SCREW   FASTENINGS. 


67 


4.  MODIFIED  TRIANGULAR  THREAD.  —  In  modern  ordnance, 
the  breech-block  is  secured  by  the  "  Interrupted  Screw  "  method, 
i.  e.,  the  outer  surface  of  the  cylindrical  block  is  threaded  to  form 
a  screw  which  engages  an  internal  thread  in  the  breech.  Neither 
thread  is  continuous,  each  being  divided  into  sectors,  12  in  large 
guns,  6  threaded  and  6  blank,  the  surface  of  the  latter  being  just 
below  the  root  of  the  thread  in  the  former.  Each  sector  is  30°  in 
length  and  all  correspond  with  similar  sectors  in  the  breech-recess 
of  the  gun.  In  closing  the  breech,  the  block  is  placed  so  that  its 
threaded  parts  are  opposite  the  blanks  of  the  recess.  It  is  then 
moved  axially  home,  turned  through  30°,  and  thus  locked  by  the 
engagement  of  the  threads. 

In  U.  S.  naval  guns  the  breech-block  thread  is  of  the  modified 
buttress  type  used  upon  armor-bolts.  Fig.  32  shows  in  profile 


the  thread  of  the  1 6-inch  U.  S.  Army  rifle.  While  the  sides  of 
the  thread  are  symmetrical  in  their  inclination  to  the  normal  to 
the  axis,  the  angle  between  them  is  large  and  there  is  a  full 
rounding  at  top  and  root.  In  this  gun  the  maximum  powder- 
pressure  is  taken  as  37,000  to  38,000  Ibs.  persq.  in.  The  dimen- 
sions of  the  block  are  : 

Diameter  of  breech-block,    D  ==  25.96"  ; 
Diameter  at  root  of  thread,  d  =  24.82  ; 
Depth  of  thread,  s  =    0.57  ; 

Pitch  of  thread,  p  =     1.71  ; 

Radius  of  rounding,  top,  r  =  o.  1 7  ; 
Radius  of  rounding,  bottom,  r^  =  o.  1 1  ; 
Length  of  threaded  portion  =  19.89  ; 


Length  of  threaded  sectors 


30°—  0.05' 


08  MACHINE   DESIGN. 

25.     Machine  and  Wood  Screws. 

1.  MACHINE  SCREWS  are  those  from  J^-in.  diameter  downward, 
used  in  metal  work.     The  head  is  slotted  and  is  either  "round" 
(spherical),  "flat"  (conical  frustum),  or  "fillister"  (cylinder  with 
spherical  top).     The  nominal  diameters  of  these  screws  are  desig- 
nated by  screw-gauge  numbers.     That  of  the  number  o  screw  is 
0.05784  in.  and  the   difference  between   consecutive  numbers   is 
0.01316  in.     Therefore,  the  nominal  (outside)  diameter  (D)  of  any 
number  (N)  may  be  found  from  the  formula : 

D  =  0.01316  N+  0.05784. 

An  assortment  of  pitches  is  given  for  each  diameter  of  screw,  in 
order  to  provide  for  the  use  of  the  same  number  with  either 
thick  or  thin  pieces,  the  latter  having  shallow  holes  and  re- 
quiring finer  pitches.  These  screws  are  described  therefore  by 
both  the  number  and  pitch.  Thus,  a  "  16-18  machine  screw" 
means  one  of  size  (screw-gauge  number)  16  and  1 8  threads  per  inch. 
At  the  meeting  of  the  American  Society  of  Mechanical  Engi- 
neers, held  in  May,  1902,  Mr.  Charles  C.  Tyler  presented  a  paper 
on  "  A  Proposed  Standard  for  Machine  Screw  Sizes."  As  to 
present  practice,  Mr.  Tyler  states  that  there  are  no  recognized 
basic  reference  standards  having  a  generally  accepted  form  of 
thread  and  diameter ;  that  the  pitches  are  apparently  stand- 
ardized only  for  the  sizes  having  even  numbers,  although  screws 
and  taps  are  furnished  for  a  number  of  different  pitches  for 
each  size ;  and  that  the  form  of  the  thread  varies  with  differ- 
ent manufacturers.  He  recommends  the  adoption  of  the  Sel- 
lers form  of  thread  and  the  computation  of  the  pitch  by  the 

formula :  

/  =  o.23  VD  +  0.625  —0.175, 

which  formula  was  proposed  by  Mr.  George  M.  Bond*  in  1882, 
and  differs  from  that  of  the  U.  S.  Standard  only  in  the  coefficient 
being  0.23  instead  of  0.24.  The  change  in  this  increases  the 
number  of  threads  per  inch  more  rapidly  as  the  diameter  decreases. 
Table  XXV.,  taken  from  Mr.  Tyler's  paper,  gives  present  practice 
and  the  modifications  suggested  by  him. 

2.  WOOD-SCREWS.  —  The   maximum   diameter  of  any  size  of 
wood-screw  is  measured  by  the  screw-gauge  given  in  the  preced- 

*"  Standards  of  Length,"  G.  M.  Bond,  1887. 


SCREW   FASTENINGS. 


69 


TABLE  XXV. 

MACHINE  SCREWS. 
(PRESENT  PRACTICE  AND  SUGGESTED  CHANGES.) 


Present  Diameters  and  Threads  per  Inch  of  Small  Machine  Screws. 
The  Difference  Between  Consecutive  Sizes  is  .01316. 

Suggested  Diameters  and 
Threads  per  Inch 
of  Small  Machine  Screws. 

|rf 

fcl-g 

-I- 

2  S'D    . 

$T°* 

^1-s 

li 

in  g 

O 

.  1  J 

IS 

Threads  also  Furnished. 

til 

IP1 

E'gtS 

J«- 

«'!! 

Pitch. 

.050 

72 

.013889 

.060 

64 

.015625 

I 

56,60,64,72. 

rV 

.07100 

.070 

60 

.016667 

ij 

56. 

A 

.07758 

.080 

56 

.017857 

2 

56 

48,64. 

A 

.08416 

.090 

52 

.019231 

3 

4 

36 

40,44,48,56. 
30,32,40,42,44,48. 

% 

.09732 
.11048 

.100 
.110 

44 

.020833 
.022727 

5 

30,32,36,40,44,48. 

1 

.12364 

.125 

40 

.025000 

6 

32 

30,36,38,40,44,48. 

A 

.13680 

.135 

40 

.025000 

7 

24,28,30,32,36,40. 

.14996 

.150 

36 

.027778 

8 

32 

24,30,36,40,44. 

A 

.16312 

.165 

32 

.031250 

9 

10 

24 

24,28,30,32. 
20,22,28,30,32,36. 

s 

.I7628\ 
.18944  / 

.180 

32 

.031250 

ii 

22,24,28,30. 

13. 

.20260 

.200 

3° 

.033333 

12 
13 

24 

20,22,26,28,30,32,34,36. 
20,22,24,32. 

ff 

•21576) 
.22892  / 

.220 

28 

•035714 

14 
15 

20 

16,18,22,24,26. 
18,20,22,24. 

.24208  I 
.25524  j 

.250 

24 

.041667 

16 

18 

16,20,22,24,26. 

6 

.26840 

11 

18 

l6,l8,20. 
16,20,22,24,26. 

ft 

.28156 
.29472 

.28125 

22 

•045455 

19 

20 

16 

16,18,20,22,24. 
18,20,22,24. 

ft 

.307881 
.32104  f 

.3125 

20 

.050000 

22 

16        18. 

II 

.34736 

•34375 

20 

.050000 

24         16       14,18,20,22,24. 

f 

.37368 

•375 

IS 

.055556 

26 

16        14. 

M 

.40000 

.40625 

18 

.055556 

28    i    14 

16. 

If 

42632 

•4375 

16 

.062500 

30 

14 

1  6. 

II 

.45264 

46875 

16 

.062500 

.500 

14 

.071429 

ing  table.  These  screws  differ  from  those  used  in  metal -work  for 
two  reasons  :  The  screw  forms  its  nut  as  it  enters  the  wood  and 
the  material  of  the  nut  is  much  weaker  than  that  of  the  screw. 
Therefore,  the  latter  is  gimlet-pointed,  its  body  tapers,  the  threads 
are  thin  and  sharp,  and  the  space  between  them  is  relatively  wide 
in  order  to  provide  a  wooden  nut-thread  of  sufficient  strength. 

26.     Pipe  Threads. 

The  standard  system  of  pipe -threads  now  used  in  the  United 
States  was  formulated  by  Mr.  Robert  Briggs  from  the  average 
usage  of  good  practice.  It  was  reported  upon  favorably  in  1886 


70 


MACHINE    DESIGN. 


by  a  committee  of  the  American  Society  of  Mechanical  Engineers, 
was  adopted  by  various  associations  of  manufacturers,  and  recom- 
mended by  the  American  Railway  Master  Mechanics'  Association. 
The  following  extract  is  taken  from  a  paper  presented  by  Mr. 
Briggs  in  the  Proceedings  of  the  Institution  of  Civil  Engineers  of 
Great  Britain,  Vol.  LXXI.: 

"  The  taper  employed  for  the  conical  tube-ends  is  an  inclination  of  I  in  32  to  the  axis. 
...  A  longitudinal  section  of  the  tapering  tube-end,  with  the  screw-thread  as  actu- 
ally formed,  is  shown  in  Fig.  33  for  a  nominal  2^-in.  tube,  /.  e.,  a  tube  of  about  2\  in. 
internal  diameter  and  2^  in.  actual  external  diameter. 


,  w   »' 


FIG.  33. 

"  The  thread  employed  has  an  angle  of  60°;  it  is  slightly  rounded  off  both  at  the  top 
and  bottom,  so  that  the  height  or  depth  of  the  thread,  instead  of  being  exactly  equal  to 
the  pitch,  is  only  §  of  the  pitch  or  o.8/w,  if  n  be  the  number  of  threads  per  inch.  For 
the  length  of  tube-end  throughout  which  the  thread  continues  perfect,  the  empirical 
formula  used  is  : 

(o.8Z>  +  4.8)/«,  (34) 

where  D  is  the  actual  external  diameter  of  the  tube  throughout  its  parallel  length  and 
is  expressed  in  inches. 

"Further  back,  beyond  the  perfect  threads,  come  two  having  the  same  taper  at  the 
bottom  but  imperfect  at  the  top.  The  remaining  imperfect  portion  of  the  screw-thread, 
furthest  back  from  the  extremity  of  the  tube,  is  not  essential  in  any  way  to  this  system 
of  joint  and  its  imperfection  is  simply  incidental  to  the  process  of  cutting  the  thread  at 
a  single  operation.  From  the  foregoing,  it  follows  that,  at  the  very  extremity  of  the 
tube,  the  diameter  at  the  bottom  of  the  thread  is  : 


"  The  thickness  of  iron  below  the  bottom  of  the  thread,  at  the  tube  extremity,  is  taken 
empirically  to  be  : 

o.oi75Z>  +  0.025.  (36) 

"  Hence,  the  actual  internal  diameter,  J,  of  any  tube  is  found  to  be  in  inches  : 

.9)/»  —  2  (o.oi75Z>  -f  0.025) 
—  o.o5Z>/«—  i.  9/«  —  0.05."  (37) 

The  proportions  of  the  Briggs  thread  are  given  in  Table  XXVI. 
As  compared  with  the  Sellers  system,  the  depth  of  the  thread  is 


SCREW   FASTENINGS. 


measured  by  a  greater  fraction  of  the  pitch  ;  but  the  latter  is  much 
finer  for  a  given  outside  diameter  and  the  thread  is  therefore  shal- 
lower and  more  suitable  for  the  thin  walls  of  a  tube. 

TABLE  XXVI. 
WROUGHT-IRON  WELDED  TUBES. 

( Briggs  Standard. ) 
TAPER  OF  CONICAL  TUBE  END  %  INCH  PER  FOOT,  OR  i  IN  32  TO  Axis  OF  TUBE. 


Diameter  of  Tube. 

Screwed  Ends. 

Thickness 
of 

Length 

Diameter 

Diameter 

Nominal 

Actual 

Actual 

Metal 

Number 

of  Perfect 

of  Bottom 

of  Top  of 

Inside, 

Inside, 

Outside, 

Inches. 

of  Threads 

Thread 

of  Thread 

Thread  at 

Inches. 

Inches. 

Inches. 

per  Inch. 

at  Bottom, 

at  End  of 

End  of  Pipe, 

Inches. 

Pipe,  Inches 

Inches.P 

i 

0.270 

0.405 

0.068 

27 

0.19 

0-334 

0-393 

f 

0.364 

0.540 

0.088 

18 

0.29 

0-433 

0.522 

g 

0.494 

0.675 

0.091 

18 

0.30 

0.567 

0.656 

0.623 

0.840 

0.109 

14 

0-39 

0.701 

0.815 

| 

0.824 

1.050 

O.II3 

14 

0.40 

0.911 

1.025 

I 

1.048 

I-3I5 

0.134 

ii  J 

0.51 

1.144          1-283 

l|- 

1.380 

1.  660 

0.140 

n| 

0-54 

1.488 

1.627 

l| 

I.6IO 

1.900 

0.145 

n|- 

0.55 

1.727 

1.866 

2 

2.067 

2-375 

0.154 

lli 

0.58 

2.200 

2-339 

2V               2.468 

2.875 

0.204 

8 

0.89 

2.62O 

2.820 

3"               3.067 

3-500 

0.217 

8 

0-95 

3-24I 

3-441 

3* 

3.548 

4.OOO 

0.226 

8 

1.  00 

3.738 

3.938 

4 

4.026 

4.500 

0.237 

8 

1.05 

4-235 

4-435 

4.508 

5.000 

0.246 

8 

1.  10 

4-732 

4-932 

5" 

5-045 

5.563 

0.259 

8 

1.16 

5-29I 

5-491 

6 

6.065 

6.625 

0.28o 

8 

1.26 

6.346 

6.546 

7 

7.023 

7.625 

0.301 

8 

1-36 

7-340 

7-540 

8 

7.982 

8.625 

0.322 

8 

1.46 

8-334 

8-534 

9 

8-937 

9.625* 

0.344 

8 

i-57 

9-328 

9-528 

10 

10.019 

10.750 

0.366 

8 

1.68 

10.445 

10.645 

27.     Stresses  in  Screw-Bolts. 

The  body  of  a  screw-bolt  may  be  regarded  as  a  cylindrical  bar, 
subjected  in  various  services  either  to  simple  tension  or  compres- 
sion or  to  one  of  these  stresses  combined  with  torsion,  or,  as  in 
the  flanged  coupling,  to  tension  and  cross-shear.  The  thread  may 
be  considered  as  a  cantilever  beam  whose  section  is  that  cut  by  a 
plane  passing  through  the  axis,  as  O-A,  Fig.  34.  The  length  of 
this  assumed  beam  is  the  depth  of  the  thread,  s;  its  depth  at  the 
support  is  p  — f,  where  p  =  pitch  and/~=  width  of  flat  at  root;  and 
its  breadth  at  the  root  is  the  developed  distance  through  which  the 
axial  section  B-C-E  extends.  This  distance,  for  one  convolution 
=  ltd  and  for  the  threads  engaged  by  a  nut  of  depth  H  ins.  and' 

*  Originally,  9.688. 


72  MACHINE   DESIGN. 

having  n  =  Up  threads  per  inch  =  nd  x  Hn.  Let  the  total  axial 
load  on  the  bolt  =  W\  the  load  per  convolution  engaged  =  W/Hn 
=  w  ;  and  the  permissible  tensile  and  shearing  stresses  per  sq.  in.= 
St  and  S,  —  o.SSt,  respectively.  Consider  the  assumed  beam  with 
regard  to  : 


i.  SHEARING  OF  THE  THREAD,  i.  e.,  "stripping"  at  the  root. 
The  shearing  force  =  W  and  is  opposed  by  the  section  of  metal  at 
the  support  or  root.  The  area  of  this  section  =  breadth  x  depth  of 
beam 

.  • .  Resistance  to  Stripping  =  W=  irdffn( p  —  /)£,.          (3 8) 

Equating  this,  for  equal  strength  throughout,  to  the  tensile  resist- 
ance of  the  bolt : 

Tensile  Resistance  =  W=T--d'LS  =  ~dHn(  p-f)S.      (39) 
4 

c  J  $pd 

"^  =  7^77 T\  •  (4°) 


In  the  Sellers  system, /  =  //8.     Substituting: 
^=0.357^. 

2.  RUPTURE  OF  THREAD  by  bending  at  the  root.    Theoretically, 
the  load  is  uniformly  distributed  over  the  surface,  which  assump- 


SCREW   FASTENINGS.  73 

tion  could  be  true  only  of  new  and  perfect  threads  ;  practically  it 
may  be  considered  as  concentrated  at  the  mean  thread  diameter. 

Therefore  :  s 

Moment  of  Load  =  W  x  -  =  M=  S//c  ; 

Section-Modulus  at  Root  =  -  =  -          5  5 

Resistance  to  Rupture  =  W  =  —     —  ^  -  -  —  '  x  -.         (41) 
Equating  (41)  and  (39)  :  pds 

ti-*u=rr  (42) 

which  expression  assumes  the  tensile  stress  in  the  bolt  and  that 
in  the  thread  due  to  flexure  to  be  of  the  same  intensity.  Substi- 
tuting the  values  for  the  Sellers  system  : 

y/=  0.637^. 

3.  BEARING  PRESSURE  UPON  THE  THREAD.  —  The  allowable 
pressure  upon  the  area  of  the  engaged  threads,  as  projected  upon 
a  plane  normal  to  the  axis,  depends  upon  the  service  of  the  screw, 
being  much  greater  with  fastenings  than  with  screws  for  the  trans- 
mission of  power,  since,  with  the  latter,  friction  and  wear  should 
be  as  small  as  possible.  The  projected  area  of  the  threads  engag- 
ing the  nut  is  (Fig.  34)  : 

_  (&  _  d*)  x  Hn. 

4 

Letting  Sb  =   permissible  bearing  stress  per  sq.  in.  : 

Permissible  Load  in  Bearing  =  W  =  -  (LP  —  d2)  HnSb.     (43) 
Equating  (43)  and  (39)  : 


(a)  Fastenings.  —  Letting  a  =  effective  area  of  bolt  and  A  =  ag- 
gregate projected  area  of  engaged  threads  : 

aS,  =  AS,     and     §  =  -.  • 
St      A 

This  stress-ratio,  the  reciprocal  of  that  in  (44),  is  given  for  the 
Sellers  system  (H  =  D)  in  Table  XXVII.  *     It  will  be  seen  that, 

*  "  Report  of  the  Board  to  Recommend  a  Standard  Gauge  for  Bolts,  Nuts  and  Screw- 
Threads  for  the  U.  S.  Navy,"  May,  1868. 


74 


MACHINE   DESIGN. 


in  this  system,  as  the  nominal  diameter  increases,  there  is  an  in- 
crease also  in  the  bearing  pressure,  the  latter  varying  from  0.242 
to  0.331  of  the  permissible  tensile  stress  per  sq.  in.  Thus,  for  a 
2-in.  bolt  of  metal  whose  ultimate  tensile  stress  is  60,000  Ibs. 
per  sq.  in.,  the  permissible  tensile  stress,  allowing  for  torsion  =  St 
=  7,000  Ibs.  per  sq.  in.  From  the  table,  Sb  /  St=  0.3046,  whence  Sb 
=  2132.2  Ibs.  per  sq.  in.,  which  pressure  is  about  the  maximum 
allowable  for  fastenings. 

TABLE    XXVII. 

RATIO  OF  BEARING  PRESSURE  TO  TENSILE  STRESS. 
(SELLERS   SYSTEM.) 


•a 

^ 

"3 

r 

1 

•3 

"3  II 

I 

'o 

•81 

V 

It 

i* 

Jl 

|| 

i$ 

*k 

R 

51 

pi 

11 

<  § 

II 

1 

1 

h 

«N 

11 

12 

§S 

W 

IE 

§ 

i 

II 

* 

i 

fc 

i 

i 

n. 

.02688 

.11105 

.242 

2    in. 

2.3019 

7-5573 

•3046 

A 

« 

.04524 

.17696 

.2556 

2i   « 

3.0232 

9.6471 

.3134 

* 

" 

.06789 
•09347 

.25536 
.34826 

.266 
.2684 

2|   « 

3.7188 
4.6224 

11.8990 
14.4881 

•3125 
.3190 

H 

.12566 

•45949 

.273 

3     " 

5.4283 

17.2221 

•3150 

/•,. 

" 

.16189 

•58461 

.2769 

3i  " 

6.5009 

20.4158 

.3188 

f 

" 

.20174 
.30190 

.72222 
1.0470 

.2795 
.288 

3l  " 

8^416 

23-5849 
27.0337 

.3200 
•3196 

1 

" 

.41969 

1.4303 

.293 

4 

9.9929 

30.8820 

•3235 

" 

•55024 

1.8813 

.3112 

11.328 

34.9236 

•3244 

ij 

11 

•69399 

2.2877 

•3033 

!< 

12.743 

40.3586 

•3157 

• 

" 

.89082 

2.94245 

.3027 

« 

14.250 

43-2728 

.3288 

i 

" 

1.0568 

3-5310 

.2993 

5      | 

15.763 

48.4000 

.3260 

" 

1.2948 

4-2507 

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17.572 

53-4950 

.3290 

« 

I-5I52 

4.9925 

•3035 

5|    | 

19.267 

58.6676 

.3280 

" 

1.7460 

5-7750 

.3023 

21.262 

62.7850 

-3286 

" 

2.0510 

6.6572 

.3081 

6      ' 

23.098 

69.8540 

•3310 

(<£)  Screws  for  Transmitting  Power  —  In  such  screws,  the  bear- 

ing  pressure  varies  within  fairly  wide  limits,  being  determined 
by  the  character  and  duration  of  the  work.  Reuleaux  gives  700 
pounds  per  square  inch  of  projected  area  for  square  and  trape- 
zoidal threads,  which  pressure  is  given  also  by  Weisbach  for 
square  threads.  Unwin  states  that  for  screws  constantly  in  motion 
this  pressure  should  not  exceed  200  pounds,  and  that  with  no 
power-screw  should  it  be  more  than  1,000  pounds. 

4.  TENSION  UNDER  STATIC  LOAD.  — Under  this  stress,  the  body 
of  a  screw-bolt   has  a  higher  elastic   limit  and  a  greater  ultimate 


SCREW    FASTENINGS.  75 

strength  than  a  cylindrical  bar  of  the  same  metal  and  of  diameter 
equal  to  that  at  the  root  of  the  thread.  These  gains  are  due  to  : 

(a)  The  Reinforcing  Action  of  the  Thread.  —  When  a  cylindri- 
cal bar  is  subjected  to  simple  tension  only,  it  is  increased  in  length 
and  contracted  in  sectional  area.  The  contraction  is  gradual,  ex- 
tends over  a  considerable  portion  of  the  specimen,  and  reaches  a 
minimum  at  the  point  where  rupture  occurs  finally.  To  permit 
the  gradual  tapering  of  the  specimen  in  unrestricted  contraction, 
the  bar  should  be  originally  of  the  same  diameter  throughout  the 
section  subject  to  elongation. 

If,  now,  there  be  turned  in  the  bar  one  or  a  series  of  parallel 
grooves  of  any  form  but  of  the  same  depth,  the  tensile  stress  and 
the  tendency  to  elongation  and  to  contraction  of  area  will  be 
greater  in  the  portions  of  lessened  diameter.  This  reduced  sec- 
tion is,  however,  insufficient  in  length  to  permit  considerable  con- 
traction ;  and,  further,  the  latter  is  resisted  by  the  metal  under 
less  stress  in  the  ridges  of  the  grooves.  In  other  words,  in  addi- 
tion to  the  lessened  distance  of  least  diameter  through  which 
stretching  occurs,  the  ridges  oppose  the  contraction  of  area  and 
the  consequent  elongation  of  the  reduced  section  and  therefore 
add  to  the  strength  of  the  latter.  As  a  result,  the  "  grooved 
specimen  "  is  stronger  under  static  tensile  load  than  a  cylindrical 
bar  having  the  same  diameter  as  that  at  the  base  of  the  grooves. 

Mr.  Kirkaldy  *  was  the  first  to  emphasize  the  effect  of  the  form 
of  a  specimen  upon  its  ultimate  strength.  In  his  report  upon  the 
Essen  and  Yorkshire  iron  plates,  he  says  : 

"When  the  breadth  of  a  specimen  is  reduced  to  a  minimum  at  one  point,  a  greater 
resistance  is  offered  to  its  stretching  than  when  formed  parallel  for  some  distance  ;  and, 
as  the  stretching  is  checked,  so  will  also  be  the  contraction  of  area  and  with  it  will 
be  an  increase  in  the  ultimate  stress." 

Table  XXVIII.  gives  the  results  of  tests  made  by  Mr.  James 
E.  Howard  f  upon  six  specimens  from  the  same  i^-in.  steel  bar,  to 
illustrate  the  effect  of  turning  a  reduced  section  or  "  stem,"  0.798 
in.  in  diameter  on  each  specimen.  Nos.  I,  2  and  3  had  cylindrical 
stems,  I  in.,  0.5  in.,  0.25  in.  long,  respectively,  connected  by  full 
fillets  to  the  body  ;  in  specimens  Nos.  4  and  5,  the  stems  were 
semicircular  grooves  of  0.4  in.  and  0.125  in.  radius,  respectively; 
a  V-shaped  groove  was  formed  in  specimen  No.  6. 

*"  Experiments  on  Wrought  Iron  and  Steel,"  1862,  p.  74. 
t  "Proceedings  International  Engineering  Congress,"  1893. 


MACHINE    DESIGN. 


TABLE  XXVIII. 
GROOVED  SPECIMENS. 


No. 

Elastic   Limit, 
Pounds  Per  Sq.   In. 

Tensile  Strength, 
Pounds  Per  Sq.  In. 

Contraction  of  Area, 
Per  Cent. 

2 

3 
4 

! 

64,900 
65,320 

68,000 
75,000 
86,000,  about. 
90,000       " 

94,400 
97,800 
102,420 
116,380 
134,960 
117,000 

49-0 

43-4 
39-6 
31-6 
23.0 
Indeterminate. 

In  Table  XXIX.  there  are  given  the  results  of  tests  made  by 
Professor  Martens  which  show  that  a  screw-bolt  under  static  ten- 
sile load  is  practically  equivalent  to  a  specimen  with  grooves 
turned  in  it  of  the  same  form  as  the  thread-groove  and  also  that 
there  was  an  average  increase  of  14  per  cent,  in  strength  for  the 
specimens  tested  over  that  of  the  cylindrical  bar  having  the  same 
diameter  as  that  of  the  root  of  the  thread.  The  table  and  the 
following  particulars  are  taken  from  Professor  J.  B.  Johnson's 
abstract  of  Professor  Martens'  paper :  * 

"Two  grades  of  mild  steel  were  used  for  these  bolts,  all  of  which  were  cut  from 
round  bars  originally  35  mm.  (1.4  in. )  in  diameter.  The  softer  material,  having  a 
tensile  strength  of  53,500  Ibs.  per  sq.  in.,  was  used  for  screw-bolts  approximately  i  in. 
in  diameter,  and  the  harder  material  having  a  tensile  strength  of  62,000  Ibs.  per  sq.  in. 
was  used  for  the  bolts  which  were  reduced  to  approximately  £  in.  in  diameter.  Four 
such  bolts  were  made  of  each  of  these  sizes  of  the  four  styles  of  thread  (sharp  V,  angle 
55°;  Whitworth ;  Sellers,  and  German  Society  of  Engineers.  The  latter  having  an 
angle  of  53°  8'  with  flats  whose  height  is  one  eighth  that  of  the  primitive  triangle), 
making  in  all  32  bolts  with  screw-threads  which  were  tested.  Two  of  each  of  these 
sets  were  tested  in  plain  tension,  the  pulling  force  being  applied  to  the  inner  face  of  the 
nut  at  one  end  and  increased  until  rupture  occurred. 

"  The  other  two  bolts  of  each  set  were  tested  also  in  tension,  but  under  a  torsional 
action  resulting  from  the  continuous  turning  of  the  nut  as  the  load  increased  to  rupture. 
In  this  case  the  distortion  resulting  from  the  permanent  elongation  of  the  bolt  was 
nearly  all  taken  up  by  the  movement  of  the  testing  machine,  the  distortion  taken  up  by 
the  turning  of  the  nut  being  the  least  possible  to  maintain  a  continuous  torsional  action 
at  this  point. 

"The  same  bars  were  also  tested  as  plain  tension-test  specimens  with  cylindrical 
bodies  and  again  with  grooves  turned  into  them  of  the  same  shape  as  the  corresponding 
screw-threads,  leaving  the  same  diameter  at  the  bottom  of  the  groove  as  obtained  at  the 
base  of  the  threads." 

The  ratio  fsa  -*-fg,  given  in  Table  XXIX.,  is  practically  unity 
showing  that  the  grooved  and  threaded  specimens  are  equal  in 
strength.  The  ratio,  fsa  -7-  test  bar,  ranges  between  no  and  119 
and  averages  114,  giving  thus  a  mean  excess  of  strength  of  14 

* Zeits,  d.  Ver.  Deuts.  Ing.,  April  27,  1895.  Abstract  by  Professor  Johnson  in 
"  Digest  of  Physical  Tests,"  July,  1896. 


SCREW   FASTENINGS. 


^    a 
X     > 

X    8 


I! 


Ml      O     C^     I-*  HH     ^ 

S^    Nfr  «    O  ON  ro 

^>    I     ^     ^     H  M     M 

•^•vO  O   "5 


Too"  < 

10^ 


t^L\O   t^v£> 


q  ts  <>vq 

0   M'  ^£>  CO 
CO   t^CO   t^ 


rtCO   ON  M   M 


«   «   o" 
vo  v£>^5  vO 


:  « 

.   .0 


77 


;S  MACHINE    DESIGN. 

per  cent,  for  the  threaded  rods  as  compared  with  cylindrical  bars 
of  the  same  net  area  of  cross-section.  These  results  apply  only 
to  static  or  gradually  applied  loads. 

It  will  be  noted  that  the  tensile  load  upon  the  cross-section  of  a 
bolt  at  the  root  of  the  thread  is  not  uniform  throughout,  since  the 
metal  of  the  latter  opposes  the  elongation  of  the  section  imme- 
diately adjacent  at  the  root,  thus  increasing  its  stress  beyond  that 
existing  at  the  axis.  It  is  apparent  that,  other  things  equal,  the 
finer  the  pitch  the  more  equable  will  be  the  distribution  of  the 
stress  upon  the  minimum  cross-section  and  the  greater  the  resili- 
ence or  internal  work  of  the  bolt  before  final  yielding.  Thus, 
Major  W.  R.  King,  U.  S.  A.,  in  experimenting  with  gradually 
applied  loads  upon  wrought-iron  bolts  of  one  and  one  half  inch 
nominal  diameter,  U.  S.  standard,  but  of  varying  pitch,  obtained 
results  as  follows  :  * 

Threads  per  Inch,  6  12  18 

Relative  Tensile  Strength,  I                       1.21  1.23 

Elongation,  0.025  0.06  0.08 

Relative  Internal  Work,  I  2.9  4 

The  U.  S.  standard  pitch  for  one  and  one  half  inch  nominal  diam- 
eter gives  6  threads  per  inch.  The  bolts  with  1 8  threads  per  inch 
were  the  stronger.  They  yielded  finally,  neither  by  stripping  nor 
by  fracture  at  the  root,  but  by  lateral  contraction,  so  that  the 
threads  of  bolt  and  nut  became  disengaged. 

(&)  Increased  Density  of  Threaded  Section.  —  Mr.  Kirkaldy  f 
found  that,  when  the  thread  was  cut  with  new  dies,  the  strength 
of  the  threaded  section  averaged  72.5  per  cent,  of  that  of  a  cylin- 
drical bar  whose  diameter  was  that  of  the  outside  of  the  thread. 
When,  however,  old  and  worn  dies  were  used,  the  average  strength 
was  increased  to  85  per  cent.  In  the  latter  case  the  tendency  of 
the  tool  is  to  force  aside  and  compress  the  metal  rather  than  to 
remove  it  by  clean  cutting,  thus  increasing  the  density  and  strength 
of  the  thread  and  adjacent  parts. 

Again,  in  bolts  threaded  by  the  "cold-pressed"  method,  no 
metal  is  removed  but  the  thread  is  raised  or  spun  above  the  body 
of  the  bolt  so  that  the  diameter  of  the  shank  is  intermediate  be- 
tween those  of  the  top  and  root  of  the  thread.  In  frequent 
tests  \  of  mild  steel  bolts  threaded  by  this  method,  fracture,  under 

* 'Trans.  Am.  Inst.  Mining  Engineers,  1885. 
f  Box  :   "  Strength  of  Materials, "  1883,  p.  12. 
J  Catalogue  Am.  Iron  and  Steel  Mfg.  Co.,  1899. 


SCREW   FASTENINGS.  79 

a  gradually  applied  tensile  load,  occurred  in  every  instance  in  the 
shank,  leaving  the  threaded  portion  intact.  The  normal  reinforcing 
action  of  the  thread  is,  by  this  process,  aided  doubtless  through  the 
compression  and  increased  density  of  the  thread  and  adjacent  metal. 

(c)  Resume.  —  The  experiments  of  Professor  Martens  show 
that,  for  static  or  gradually  applied  loads,  the  ultimate  strength 
of  the  section  at  the  root  of  the  thread  is  14  per  cent,  greater 
than  that  of  a  cylindrical  bar  of  the  same  metal  and  cross-section. 
This  increase  in  strength  is  due  to  the  reinforcing  action  of  the 
thread,  and,  in  some  degree,  to  the  greater  density  of  the  metal. 
Under  sudden  and  repeated  stresses,  however,  the  results  would 
probably  be  less  favorable,  owing  to  the  appreciable  concentration 
of  the  stress  about  the  bottom  of  the  groove  which  would  produce 
fracture  at  the  reentrant  angle.  The  increase  in  strength  of  the  screw 
from  these  causes  is,  therefore,  not  considered  in  designing  bolts. 

5.  TENSION  UNDER  SUDDEN  LOADS  OR  IMPACT-.  —  In  both  ma- 
chinery and  structures  a  bolt  may  be  required  to  withstand  not 
only  the  tensile  stress  of  a  gradually  applied  or  static  load  but 
also  that  produced  by  a  suddenly  applied  load  or  by  impact. 
Examples  of  such  requirements  may  be  found  in  bridge  work,  in 
marine  machinery,  in  rock  drills,  etc. 

Let  the  static  or  gradually  applied  load,  P,  produce  in  the  bolt 
a  total  stress,  P,  and  elongation,  /.  Then,  the  same  load,  if  sud- 
denly applied,  will  produce  a  maximum,  momentary,  total  stress, 
2P,  and  elongation,  2X,  which,  after  a  series  of  axial  oscillations  of 
the  bolt,  will  be  reduced,  when  the  latter  comes  to  rest,  to  the 
final  stress,  P,  and  elongation,  ),,  due  to  P  as  a  static  load.  In 
impact,  the  load,  P,  is  assumed  to  act  as  if  it  were  not  only  sud- 
denly applied  but  in  motion  with  a  velocity,  v,  such  as  would  be 
acquired  by  fall  through  a  height,  h.  Under  these  conditions, 
P  produces  a  maximum,  momentary,  total  stress,  Q,  and  elonga- 
tion, y,  which,  when  -the  bolt  after  oscillation  comes  to  rest,  are 
reduced  to  P  and  ^,  respectively.  Disregarding  the  weight  and 
consequent  inertia  of  the  bolt,  we  have  :  * 


y*l\i  +  < 

r~*    \ 
sl2i+I> 

(45) 
(46) 

*Merriman,  "Mechanics  of  Mechanics,"  1900.     Art.  93. 


80  MACHINE    DESIGN. 

When  h  =  o,  these  formulae  become  : 

Q=2P      and    y  =  2)., 

i.   e.,   the  values    for  a    load  suddenly  applied  but  without  im- 
pact. 

In  the  three  cases  cited,  the  total  final  stress  is  P.  For  this 
stress,  the  absolute  requirement  is  that  the  area,  a,  of  the  mini- 
mum cross-section  of  the  bolt  shall  be  such  that  the  unit  stress, 
Pja,  shall  not  exceed  the  working  stress  of  the  metal.  The 
strength  of  this  minimum  section  is  therefore  practically  the 
measure  of  the  resistance  of  the  bolt  to  safe  static  stress. 

Work  is  the  product  of  a  resistance  by  the  distance  through 
which  the  latter  is  overcome.  The  external  work  of  impact, 
P(1i-\-y),  is  resisted  by  the  elastic  resilience  or  internal  work, 
YZ  Q  X  y,  of  the  bolt.  The  same  internal  work  may  be  the  prod- 
uct of  a  high  average,  total  stress,  y2Q,  and  a  small  elongation 
y,  or,  conversely,  of  a  low  stress  and  a  large  elongation. 
Under  the  conditions  given,  it  is  apparent  that  the  elastic  resilience 
is  the  measure  of  the  resistance  of  the  bolt  to  sudden  or  impul- 
sive stress. 

In  order  to  secure  maximum  total  elongation  under  sudden  load 
and  therefore  the  least  value  of  <2,the  sectional  area  of  the  unthreaded 
portion  of  the  bolt  should  be  the  minimum  permissible,  i.  c.,  that 
at  the  root  of  the  thread,  which  minimum  area  is  determined  by 
the  static  load.  The  minimum  section  should  extend  through 
as  great  a  portion  of  the  bolt  as  possible,  since  the  total  elonga- 
tion depends  upon  its  length.  When  the  area  at  any  point  is 
greater  than  the  minimum,  the  unit  stress  over  that  area  is  less 
than  over  the  latter  and  the  elongation  of  that  part  and  therefore 
of  the  bolt  will  be  reduced  proportionately  and  there  will  be  an 
increase  in  the  average  stress. 

Equating  the  external  and  internal  work,  we  have  for  a  bar  of 
sectional  area  A,  length  L,  and  maximum  total  and  unit  stresses, 
Q  and  q,  respectively  :  2 

K=\qE-AL,  (47) 

on  which  K  is  the  internal  work  or  elastic  resilience  and  E  is  the 
modulus  of  elasticity  for  tension. 

Consider  two  bolts  of  the  same  total  length,  length  of  shank, 
and  area,  a,  at  the  root  of  the  thread.  In  : 


SCREW   FASTENINGS. 


81 


Bolt  No.  i :  Let  the  length  of  threaded  portion  be  /  and  its 
minimum  sectional  area  and  maximum  unit  stress  be  a  and  q,  re- 
spectively. Let  the  length  of  shank  be  kl  and  its  sectional  area  be 
na.  Then,  the  maximum  unit  stress  in  the  shank  will  be  : . 

«.?_z. 

an  n 

Bolt  No.  2  :  As  before,  total  length  =  /  +  kl  =  I  (i  +  k\  Let 
the  uniform  sectional  area  throughout  screw  and  shank  (disregard- 
ing thread  ridges) =a  and  the  maximum  unit  stress  throughout=^r 

The  elastic  resilience  of  each  bolt  will  be  the  sum  of  the  internal 
work  of  its  threaded  portion  and  shank.  From  (47),  we  have  for  : 

Bolt  No.  i  : 


2EK       n 


Bolt  No.  2  : 


(h 


K=y^ 


(48) 


(49) 


2EK 


al       i  -f  k 


\2hK         n 
=  \    a/    '  «T 


nk' 


Assuming  the  total  work,  K,  as  the  same  in  each  case,  it  will  be 
seen  that  ql<.g,  i-  c.,  that,  by  making  the  shank  of  the  same 
sectional  area  as  that  at 
the  root  of  the  thread, 
the  maximum  unit  stress 
upon  the  bolt  has  been  re- 
duced. The  equations  dis- 
regard the  increase  of  area 
due  to  the  thread  ridges, 
which  increase,  for  accur- 
acy, should  be  included. 
When  there  is  no  impuls- 
ive load  and  a  rigid  connec- 


E 


FIG.  35. 


tion  is  required,  there  is  no  advantage,  possibly  the  reverse,  in 
increasing  the  elastic  resilience  of  the  bolt  by  decreasing  the  cross- 
section  of  the  shank. 


82  MACHINE   DESIGN. 

In  reducing  its  section,  the  shank  may  be  turned  down  on  the 
outside  to  the  diameter  at  the  root  of  the  thread  or  it  may  be 
drilled  axially  from  the  head  inward  to  the  point  where  the  thread 
begins,  both  as  in  Fig.  35.  The  latter  method  is  preferable,  since 
it  leaves  a  section  which  is  the  stronger  of  the  two  in  torsion. 
The  shearing  stress  at  any  point  of  a  section  varies  directly  as  the 
distance  of  that  point  from  the  axis,  but  the  resisting  moment  of 
that  stress  with  respect  to  the  axis  varies  directly  as  the  square 
of  that  distance.  Therefore,  a  given  area  of  section  is  most 
economically  used  with  regard  to  torsion  by  so  disposing  it  that 
its  fibres  shall  be  remote  from  the  axis. 

Professor  Sweet,*  in  testing  solid  and  drilled  bolts,  i^  in.  nom- 
inal diameter  and  12  ins.  long,  found  that,  under  gradually  ap- 
plied load,  the  undrilled  bolt  broke  in  the  thread  with  an  elonga- 
tion of  ^  in.,  while  the  drilled  bolt  was  fractured  in  the  shank  after 
a  total  elongation  of  2\  ins.  Assuming  the  same  mean  load  in 
each  case,  the  ultimate  resilience  of  the  drilled  bolt  was  9  times 
that  of  the  other.  "  Drop  tests,"  i.  e.,  those  producing  tensile 
shock,  gave  similar  results. 

6.  FRICTION  OF  THE  SCREW. — The  screw-thread  is  essentially 
an  inclined  plane  wrapped  around  a  cylinder,  as  on  the  bolt,  or 
within  a  hollow  cylinder,  as  in  the  nut.  If  the  bolt  be  vertical, 
the  wrench  engages  the  nut  in  a  horizontal  plane  and  the  axial 
load  upon  the  bolt  may  be  assumed  as  raised  vertically  by  move- 
ment along  the  inclined  plane  of  the  nut-thread,  the  force  acting 
horizontally.  The  efficiency  of  the  screw,  per  se,  and  that  of  the 
inclined  plane  are  the  same.  Sliding  friction  is  generated  between 
the  bolt  and  nut  threads  as  they  move  upon  each  other.  The 
resistance  or  force  of  this  friction  acts  along  the  contact-surfaces  in 
opposition  to  the  direction  of  relative  motion  of  the  latter.  The 
magnitude  of  this  force  is  measured  by  the  product  of  the  coeffi- 
cient of  friction  and  the  total  normal  pressure  between  the  surfaces. 

Thread -friction  not  only  reduces  the  useful  work  and  efficiency 
of  the  screw,  but  also  adds  to  the  torsional  stress  within  the  body 
of  the  bolt  produced  by  the  component  of  the  load  which  is  nor- 
mal to  the  axis.  Therefore,  the  bolt  is  subjected,  in  screwing  up, 
to  torsion  due  to  the  nut  and  to  tension  or  compression  from  the 
axial  load.  The  combined  stress  thus  developed,  exceeds  mate- 
rially the  simple  axial  stress  when  the  nut  is  screwed  home  and  at 

*A.  W.  Smith,   "Machine  Design,"  1895,  P-  135- 


SCREW    FASTENINGS.  83 

rest.  This  torsional  action  is  of  especial  importance  in  small  screws, 
which  may  readily  be  sheared  by  excessive  force  upon  the  wrench. 

In  addition  to  the  friction  of  the  threads,  the  efficiency  of  the 
screw  is  reduced  further  by  the  friction  of  the  rotating  member  of 
the  pair  —  the  nut  or  screw,  as  the  case  may  be — upon  its  sup- 
port. Again  if,  as  is  usual,  the  turning  moment  is  applied  at  one 
side  only  and  not  as  a  couple,  there  is  a  lateral  thrust  upon  the 
support  with  a  frictional  resistance  similar  to  that  of  a  journal. 

(a)    Torsion  due  to  Thread  Friction.  —  The  pressure   upon  the 


FIG.  36. 

threads  in  computations  respecting  friction,  may  be  taken  as  con- 
centrated upon  the  mean  helix  or  the  circumference  of  the  mean 
thread-diameter,  d^  of  pitch-angle,  <50  (Figs.  22  and  36).  Each 
element  of  the  thread-surface  is  regarded  as  sustaining  an  equal 
elementary  portion  of  the  total  axial  load  or  stress,  W,  and  each 
element  has,  therefore,  a  frictional  resistance  of  the  same  magnitude. 


84  MACHINE   DESIGN. 

Since  the  conditions  for  all  elements  are  thus  identical,  the  total  ex- 
ternal forces  and  thread-resistances  may  be  assumed  to  be  concen- 
trated at  a  single  point  upon  the  circumference  of  diameter,  dy 

In  Fig.  36,  taking  the  nut  as  the  turning  member,  let  A-B-C 
be  the  inclined  plane  formed  by  developing  one  convolution  of  the 
nut  thread  of  diameter,  d^.  Let  A-B  be  that  thread  and  E-G  a 
portion  of  the  bolt-thread.  The  base  of  the  plane  is  xd0,  the 
height  is  the  pitch,  /,  and  the  pitch-angle,  o0  =  B-A-C.  Consider 
the  external  rotating  force  as  applied  in  a  plane  normal  to  the 
axis  and  as  tangent  to  the  mean  thread-circumference.  Let : 

W  =  total  axial  load  or  tension  in  bolt ; 

P0  =  external  force  to  raise  W  without  friction  ; 
P=  external  force  to  raise  Wwith  friction  ; 

Pl  =  external  force  to  lower  W  with  friction  ; 

N  =  direction  of  thread -pressure,  without  friction  ; 

R  =  direction  of  thread-pressure,  raising,  with  friction  ; 

Rl  =  direction  of  thread-pressure,  lowering,  with  friction  ; 
JJL  =  coefficient  of  thread-friction  =  tan  <p  ; 
(f  =  angle  of  repose  or  of  friction  ; 

F  •=.  total  force  of  thread -friction  in  raising  W '=  N  tan  <p  ; 

F^  =  total  force  of  thread-friction  in  lowering  W  =  N  tan  <f. 

Square  Threads.  —  Consider  the  force  upon,  and  the  resist- 
ance of,  the  nut-thread,  A-B.  To  raise  W,  the  latter  must  move 
to  the  left ;  to  lower  it,  to  the  right.  The  resistances  of  the 
thread  to  these  movements  are  the  components  normal  to  the 
axis  of  ^Vand  /''and  N  and  Fl  respectively,  which  resistances  must 
be  equal  to  the  corresponding  and  parallel  applied  forces,  P  and  Pr 

In  raising  W  without  friction  : 

N  is  normal  to  the  thread.  The  resistance  is  its  component 
normal  to  the  axis  and  opposing  P0,  which  component  is 

a-b  —  o-a  tan  SQ  =  If7  tan  d0  =  Py  (50) 

In  raising  Wwith  friction  : 

The  resistances  are  the  components,  normal  to  the  axis,  of  N 
and  F.  The  latter  =  pN=  N  tan  c.  The  resultant  of  N  and  F 
is  R,  making  the  angle  <p  with  N.  The  component  of  R,  normal 
to  the  axis  and  opposing  P  is 

a-c  =  O-a  tan  (<p  +  ofl)  =  W  tan  (<p  +  d0)  =  P.  (51) 


SCREW   FASTENINGS. 


From  (50)  and  (5 1)  it  will  be  seen  that  the  resistance  of  friction  is 
equivalent  to  increasing  the  angle  fi-A-Cof  a  frictionless  plane  by  <p°. 

In  lowering  W  with  friction  : 

The  resistance  are  the  components,  normal  to  the  axis,  of  N  and 
Fr  The  latter  =  pN  =  N  tan  <f>.  The  resultant  of  N  and  Fl  is 
Rv  making  the  angle  <p  with,  and  lying  to  the  left  of,  N.  If 
<p  >  30,  the  angle  between  R^  and  the  axis  is  <p  —  d0,  and  the  com- 
ponent of  Rl  normal  to  the  axis  and  opposing  Pv  is 

a-d  =  o-a  tan  (<p  —  OQ)  =  W  tan  (<p  —  dQ)  =  Pr  (52) 

In  "  overhauling  "  screws,  the  pitch  is  so  coarse  that  the  load 
is  capable  of  reversing  and  lowering  the  screw.  If,  in  (52), 
30  =  (f,  then  will  tan  (y>  —  <J0)  =  o  /.  Pl  =  o.  The  pitch-angle  is 
then  equal  to  the  angle  of  repose  and  no  force  will  be  required 
either  to  lower  the  load  or  to  hold  it  in  equilibrium.  If,  as  in  Fig. 
36,  a,  o0  >  <p,  then  Rv  the  result- 
ant of  N  and  Flt  will  lie  to  the 
right  of  the  axis  and  its  compo- 
nent normal  to  the  axis  will  be  e-a, 
which  acts  in  the  direction  of  the 
lowering  force,  Pr  Therefore,  the 
screw,  if  not  sustained  by  a  force, 
P,  will  overhaul,  with  a  torque 
equal  to  the  product  of  W  tan 
(<J0  —  <p)  by  its  leverage,  dj  2. 
Screws  of  this  type  are  met  infre- 
quently and,  as  a  rule,  in  light 
mechanisms  only.  Usually,  JJL  lies 
between  o.  10  and  0.20,  giving  val-. 
ues  of  if  of  about  5°  45'  and  1 1° 
30',  respectively.  In  Table  XIX., 
for  ^-in.  and  4-111.  screws,  d0  is  about  8°  45'  and  3°  15',  respec- 
tively. These  values  are  for  square-threaded,  power-screws  whose 
pitch  is  twice  that  of  corresponding  screws  of  the  U.  S.  Standard. 

Triangular  Threads.  — In  Fig.  37,  let  N  and  N'  be  the  normal 
pressures  upon  square  and  triangular  threads,  respectively.  Then 
N'  =  N  sec  /9,  in  which  /?  is  the  base-angle.  Letting  F1  =  the 
frictional  resistance  of  a  triangular  thread,  we  have,  since  for  the 
square  thread,  F=  pN: 

F'  =  pN'  =  (JJL  sec  fi}N=F  sec  /?. 


FIG.  37. 


86  MACHINE    DESIGN. 

As  compared  with  the  square  thread  of  the  same  pitch-angle, 
the  friction,  F' ,  is,  therefore,  sec  ft  times  greater.  Hence,  the  re- 
sisting component,  normal  to  the  axis,  will  be  increased  propor- 
tionately; and,  in  the  formulae  leading  to  equations  (51)  and  (52), 
we  may  replace  //  by  p  sec  ft.  From  these  equations,  we  have : 

P==  W.   ten  P  +  tan  *o    =  W.    P  +  ten  *o   =  W.  ^d*  +  P. 
I  —  tan  (p  tan  30  i  —  p.  tan  d0  xd^  —  pp' 

and,  similarly,  p  =  w  fwd0  -  / 

1  '*<  +  /'/ 

Replacing  fj.  by  p  sec  ft  : 

p_wP**cfad*+P  (     , 

V  ro/0->sec#' 

pace  fad, -fi 

^-    r^0  +  ^sec^' 

These  are  the  equations  for  the  raising  and  lowering  forces,  P 
and  Pv  respectively,  which,  considering  friction,  require  to  be  ap- 
plied tangentially  to  the  mean  thread  circumference  of  a  triangular- 
threaded  screw.  The  form  of  the  equations  is  that  given  by  Unwin. 
In  the  Sellers  system,  ft  =  30°  and  sec  ft  =  1.15.  Substituting : 

p=w.^J^±± 

K-  i.is  &' 

Pi=W.^^~P,  (56) 

7r^0-f  1.15^ 

Thus,  the  ^-in.  bolt  has,  in  this  system,  the  maximum  inclination 
of  the  thread  and  hence  the  greatest  tendency  to  be  sheared  by 
torsion.  For  this  bolt, 

D  -(-  d      0.25  +  0.185 
p  =  0.05  and  d0  = = -=  0.2175. 

Taking  //  =  o.  1 24  : 

P=0.22W. 

With  an  ultimate  tensile  strength  of  bolt-metal  of  60,000  Ibs.: 

red'1 

W  = x  6o,OOO  =  1,613  Ibs.; 

4 

P=  1613  x  0.22  =  355  Ibs., 

i.  e.,  a  force  of  355  Ibs.  applied,  under  the  conditions  as  above,  to 
a  J-in.  screw-fastening  will  rupture  the  latter  by  tensile  stress. 


SCREW   FASTENINGS.  8/ 

The  assumed  value  of  ft  is  suitable  only  for  accurately  fitting,  well- 
lubricated  threads.  Owing  to  viscidity  of  the  lubricant,  the  pres- 
ence of  foreign  matter,  or  rough  surfaces  from  abrasion,  the  coeffi- 
cient will  be  usually  much  higher  with  a  corresponding  increase 
in  friction  and  torsional  stress. 

(£)  Coefficients  of  Friction  for  Screw -Threads.  —  In  average  cases, 
the  value  of  //  is  taken  as  0.15.  This  assumes  fair  conditions  of 
surface  and  lubrication.  Under  other  circumstances  the  coefficient 
may  reach  0.40  or  more.  Professor  Albert  Kingsbury  *  has  con- 
tributed to  the  meager  knowledge  available  upon  this  question, 
the  results  of  valuable  experiments  conducted  by  him  and  apply- 
ing especially  to  slow-moving  power-screws. 

The  tests  were  made  upon  a  set  of  square-threaded  screws  and 
nuts  of  materials  as  given  in  Table  XXX.  and  of  dimensions  as 
follows  : 

Outside  Diameter  of  Screw          ...        .    .  1.426  inches. 

Inside  Diameter  of  Nut  1.278      " 

"  Mean  Diameter  "  of  Thread I-352      " 

Pitch  of  Thread      333       " 

Depth  (effective)  of  Nut 1.062       " 

The  nuts  fitted  the  screws  very  loosely,  so  that  all  friction  was 
excluded  except  that  on  the  faces  of  the  threads  directly  supporting 
the  load.  Four  sets  of  tests  were  made.  The  maximum  total  load 
was  14,000  pounds  in  all  tests  excepting  No.  4,  in  which  it  was 
4,000  pounds.  Readings  were  taken  at  pressures  given  in  the 
table.  The  total  bearing  area  of  thread  was  approximately  one 
square  inch,  so  that  the  total  axial  load  was  equal  to  the  pressure 
per  square  inch  upon  the  thread. 

The  lubricants  were  a  purely  mineral  "  Heavy  Machinery  Oil  " 
of  specific  gravity,  0.912,  and  "Winter  Lard  Oil"  of  sp.  gr., 
0.919.  The  former,  in  test  No.  3,  was  mixed,  in  equal  volumes, 
with  graphite,  the  brand  being  Dixon's  "  Perfect  Lubricator." 
The  screws  and  nuts  were  flooded  with  lubricant  immediately 
before  the  tests. 

The  threads  were  carefully  cut  in  the  lathe  and  had  been  worn 
down  to  good  condition  by  previous  trials.  Screw  No.  5  was  not 
quite  so  smooth  as  the  others.  The  speed  was  very  slow,  being 
about  one  revolution  in  two  minutes  and  the  motion,  in  tightening 
especially,  was  also  somewhat  irregular,  so  that  the  action  between 

*  Trans.  Am.  Soc.  Meek.  Engs.,  Vol.  XVII. 


88 


MACHINE   DESIGN. 


screw  and  nut  was  quite  similar  to  that  occurring  when  machine- 
bolts  are  set  up  in  comparatively  unyielding  material.  The  re- 
sults are  given  in  Table  XXX.  Each  figure  in  test  No.  i  is  the 
average  of  eight  readings ;  in  the  remaining  tests,  of  four  readings. 

TABLE  XXX. 
COEFFICIENTS  OF  FRICTION  FOR  SQUARE  THREADS. 


Screws. 

Nuts. 

6 
Mild 
Steel. 

Wr/ught 

8 
Cast 
Iron. 

cast 

Brass. 

I.  Mild  Steel. 
2.  Wrought  Iron. 
3.  Cast  Iron. 
4.   Cast  Bronze. 
5.  Mild  Steel,  Case  Hardened. 

O.I4I 
0.139 
0.125 
0.124 
0.133 

0.16 
0.14 
0.139 

0.135 
0.143 

0.136 
0.138 
O.II9 
0.172 
O.I3 

0.136 
0.147 
O.I7I 
0.132 
0.193 

TEST  No.   i. 
Heavy  Machinery 
oil. 
Pressure,     10,000 
Ibs.  per  sq.  in. 

2. 

3- 
4- 
5- 

0.12 
O.II25 
0.10 

0.115 
0.1175 

0.105 
0.1075 

O.IO 
0.10 

0.0975 

O.IO 
O.IO 

0.095 

O.I  I 

0.105 

O.II 
0.12 
O.II 
0.1325 
0.1375 

TEST  No.  2. 
Lard  oil. 
Pressure,     1  0,000 
Ibs.  per  sq.  in. 

2. 

3- 
4- 
5- 

O.I  1  1 

0.089 
0.1075 
0.071 
0.1275 

0.0675 

0.07 
0.071 

0.045 
0.055 

0.065 
0.075 
0.105 
0.044 
0.07 

0.04 
0.055 
0.059 
0.036 
0.035 

TEST  No.  3. 
Heavy  Mach'y  oil 
and  Graphite. 
Pressure,     10,000 
Ibs.  per  sq.  in. 

2. 

3- 
4- 
5- 

0.147 
0.15 
0.15 

0.127 

0.155 

0.156 

0.16 

0.157 
0.13 

0.1775 

0.132 
0.15 

0.14 

0.13 

0.1675 

0.127 
O.II7 
O.I2 
0.14 
0.1325 

TEST  No.  4. 
Heavy  Machinery 
oil. 
Pressure,  3,000 
Ibs.  per  sq.  in. 

Professor  Kingsbury's  conclusions  are  : 

"  That,  for  metallic  screws  in  good  condition,  turning  at  extremely  slow  speeds,  under 
any  pressure  up  to  14,000  Ibs.  per  square  inch  of  bearing  surface  and  freely  lubricated 
before  application  of  the  pressure,  the  following  coefficients  of  friction  may  be  used  : 


COEFFICIENTS  OF  FRICTION. 


Lubricant. 

Minimum. 

Maximum. 

Mean. 

Lard  Oil, 

0.09 

0.25 

O.II 

Heavy  Machinery  Oil  (Mineral), 

O.II 

0.19 

0.143 

"     and            I 
graphite  in  equal  volumes,      / 

0.03 

0.15 

0.07 

With  regard  to  the  value  of  the  coefficient  to  be  used  in  design- 
ing power-screws,  Professor  Kingsbury  says  : 

"  That  (the  value)  depends  upon  the  object  of  the  design.    If  the  screw  is  to  be  made 
so  that  it  could  not  overhaul  under  the  most  favorable  conditions,  with  either  lard  oil  or 


SCREW   FASTENINGS. 


89 


FIG.  38. 


heavy  machinery  oil,  probably  8  per  cent,  would  be  the  highest  allowable  coefficient ; 
and,  for  a  certain  margin  of  safety,  a  somewhat  lower  figure.  If  the  driving  mechan- 
ism is  to  be  designed  with  a  view  to  making  the  screw  turn,  even  if  perfectly  dry,  prob- 
ably 30  or  40  per  cent,  would  be  the  figure.  If  the  amount  of  power  likely  to  be  lost 
in  the  long  run  is  what  is  wanted,  probably  15  per  cent,  would  be  a  safe  coefficient  for 
everyday  work.  This  might  be  reduced  to  10  per  cent,  with  lard  oil  under  the  best 
conditions  and  at  the  speeds  used  in  these  experiments. ' ' 

Mr.  Wilfred  Lewis  states  that,  "  for  feed  screws  which  turn 
slowly,  [JL  =  o.  1 5  may  be  taken  as  a  good  gen- 
eral average." 

(c)  Friction  of  the  Support. — The  thrust  of  a 
power-screw  may  be  taken  by  the  end  of  the 
screw  itself  upon  a   plane   step-bearing  whose 
maximum   diameter   is  equal    to   the    effective 
diameter,  d,  of  the  screw  or  the  thrust  may  be 
borne  by  an  annulus  forming  a  collar-bearing 
at  the  end  of  the  threaded  portion.    Both  types  of 
bearing  are  indicated  in  Fig.  38.     In  fastenings, 
the  thrust  and  force  of  friction  act  between  the 
under  surface   of  the  nut  and  the  washer,  the 
leverage  of  the  force  being  about  two   thirds 
the  nominal  diameter,  D,  of  the  bolt.     Let  : 
W  =  total  axial  load  ; 
p.'  =  coefficient  of  friction  ; 
Wfjf  =  force  of  friction  j 

r  •=  radius  of  plane  step  bearing  of  diameter,  d\ 
Rl  and  R2  =  outer  and  inner  radii,  respectively,  of  collar-bearing ; 

R  =  2^  D  =  leverage  of  Wfi!  in  nut. 
Then,  the  moment  of  the  friction  in  the  : 

Step  Bearing  =  W/JL'-  %r;  (57) 

E>  3         r>  3 

Collar  Bearing  =  Wa'-  %  •  -  ~ ^  ;  (58) 

K\  —  Ki 

Nut  —  Wpr  •%  D.  (59) 

The  reduction  of  the  moment  by  the  use  of  a  step-bearing  is  ap- 
parent. This  form,  however,  produces  the  most  uneven  wear 
and  usually  the  greatest  unit  pressure. 

In  addition  to  the  vertical  load  there  is  usually  a  sidewise 
thrust  on  the  screw-support,  since  the  power  is  generally  applied 
as  a  single  force  and  not  as  a  couple.  This  produces  lateral  pres- 


90  MACHINE   DESIGN. 

sure  and  friction  between  the  threads  or  shank  of  the  screw  and 
the  support  or  nut  and  connected  parts.  The  action  resembles  that 
of  a  shaft  journal.  Views  as  to  the  distribution  of  friction  in  the 
latter  are  somewhat  conflicting.  In  practice,  the  total  pressure  is 
assumed  to  be  divided  uniformly  over  the  projected  area  of  the 
bearing  surface. 

7.  COMBINED  TORSIONAL  AND  TENSILE  OR  COMPRESSIVE 
STRESSES.  —  The  axial  load  upon  a  screw  produces  a  tensile  or 
compressive  stress  and  the  external  force  applied  to  the  nut  in 
order  to  raise  the  load,  develops  a  shearing  stress.  Disregard- 
ing the  reinforcing  action  of  the  thread,  both  stresses  may  be 
assumed  as  acting  upon  the  effective  area  only  of  the  bolt.  Then, 
the  unit  tensile  stress  will  be  equal  to  the  total  load  divided  by 
the  effective  area  and  the  unit  shearing  stress  at  the  outer.circum- 
ference  of  the  area  —  where  that  stress  is  a  maximum  —  will  be 
equal  to  the  twisting  moment  divided  by  the  polar  modulus  of 
the  section.  Referring  to  Fig.  36,  the  twisting  moment  is  P  x 
4/2.  Then : 

Unit  tensile  stress  =  W -±-  - —  =  S  ;  (60) 

4 

Unit  shearing  stress  =  P^.~  =  ~^  =  St.          (6 1 ) 

These  stresses  coexist  and  combine  to  produce  a  maximum,  unit 
tensile  stress  upon  a  plane  whose  angle  with  the  axis  depends 
upon  their  relative  magnitude.  Similarly,  they  combine  to  pro- 
duce a  maximum  unit  shearing  stress  upon  a  plane  whose  angle 
differs  from  that  of  the  first  but  is  governed  by  similar  conditions. 
Evidently,  the  required  effective  area  will  depend  upon  the  inten- 
sity of  these  resultant  stresses,  the  formulae  for  which  are  : 


Maximum  tensile  unit  stress  =  |-  St  +  V  -S*  +  ^^2  =  St  max.;  (62) 


Maximum  shearing  unit  stress  =  y  S*  +  ^St2  =  Ss  max.  (63) 

When  a  screw  which  is  so  short  that  it  may  be  treated  as  a  strut, 
is  under  compression,  the  maximum  compressive  and  shearing  unit 
stresses  may  be  found  by  replacing  St  in  (62)  and  (63)  by  the  unit 
compressive  stress.  In  designing  a  screw  for  a  given  load,  the 
maximum  stresses,  as  above,  must  not  exceed  the  elastic  strength 
of  the  metal.  The  usual  practice,  as  given  in  §  29,  is  to  assign  a 
reduced  working  stress  to  the  material  as  the  diameter  decreases. 


SCREW   FASTENINGS. 


The  experiments  of  Professor  Martens  —  the  results  of  which 
are  given  in  Table  XXIX.  — show  the  weakening  of  the  effective 
section  of  the  bolt  to  axial  tensile  load  which  results  from  the 
torsional  action  of  the  nut.  His  conclusions,  from  these  tests, 
are  : 

"  The  weakening  effect  of  the  turning  of  the  nut  under  stress  at  rupture,  is  much  less 
than  might  have  been  predicted,  when  the  distortion  of  the  screw  below  the  nut  by  per- 
manent elongation  is  taken  into  consideration.  The  tests  indicate,  for  this  case,  a 
strength  of  the  I  -in.  bolts  about  20  per  cent,  less  than  that  of  the  plain  bars  and  of  the 
^-in.  bolts  about  15  per  cent,  less  than  that  of  the  plain  bars.  In  general,  it  may  be 
said  that  the  turning  of  the  nut  upon  the  bolt  at  rupture  reduces  the  strength  of  the  nut 
section  of  the  bolt  by  about  30  per  cent." 

8.   CROSS  SHEAR.  —  In  the  flange  coupling  shown  by  Fig.  39, 
the  bolts  transmit  the  torsional  stress  from  one  section  of  the  shaft 
to  the  next,  and,  if  accurately 
fitted  to  the   bolt-holes,  are 
exposed  practically  to   cross 
shear    only,   there   being    no 
bending  stress  and  the  tensile 
load,    due    to   drawing   the 
flanges  together,  being  rela- 


tively   slight.      The    usual 
method  of  design  is  to  assume 


FIG.   39. 


the  diameter  of  the  bolt  circle  and  equate  the  resistances  to  shear- 
ing of  the  shaft  and  bolts,  the  result  being  an  equation  in  terms  of 
the  diameter  and  number  of  the  latter.     Let : 
R  =  radius  of  centre  of  bolt-holes ; 
D  =  diameter  of  shaft ; 
d  =  diameter  of  bolts  ; 
n  =  number  of  bolts  ; 

T. M.  =  maximum  twisting  moment  on  shaft ;  (force,  7!jP.) 
R. M.  =  resisting  moment  of  shaft ; 
T.'M.'  =  twisting  moment  at  bolt  centres  ;  (force,  T.'F.') 

R.S.  =  aggregate  resistance  of  bolts  to  shearing. 
The  resisting  moment  to  shearing  of  a  circular  section  is  equal 
to  the  product  of  the  shearing  stress,  Sf,  at  its  periphery  by  the 
polar  modulus  of  the  section,  ~d3/i6,  where  d  is  the  diameter. 
T.F.  is  expressed  in  terms  of  the  unit  radius  and  will  be  to  T.'F.' 
inversely  as  their  respective  radii.  We  have : 


92  MACHINE   DESIGN. 

T.M.  =  R.M.  =  r~  -  S  ' 

ID 


T.'F'  :  T.F.  ::  i  :  R  .:  T.'F.'  =  =    ~D  •  S  ; 

K  IDA. 

-d2 
R,S.  =  --  x  n  x  Sf 

Equating  the  values  of  T.'F.'  and  R.S.: 


To  allow  for  inaccurate  fitting  and,  therefore,  for  slight  bending, 
the  shearing  stress  on  the  bolts  is  usually  made  three  fourths  of 
that  on  the  shaft.  Introducing  this  fraction  : 


R  is  usually  0.75  to  O.8  times  D.  The  number  and  diameter  of 
the  bolts  are  interdependent.  If  it  be  desired  that  the  outside 
diameter  of  the  coupling  shall  be  as  small  as  possible,  n  should 
be  increased  and  d  decreased,  n  is  usually  a  multiple  of  the  num- 
ber of  duplicate  sections  of  the  crank-shaft.  The  bolts  may  be 
either  headless  taper  bolts  or  "  body-bound  "  and  cylindrical  with 
heads,  as  shown  in  Fig.  39.  With  the  former  type  the  weight  of 
the  head  is  saved  and  a  rigid  joint  ensured.  The  objections  to  it 
are  the  accurate  fit  required,  and,  owing  to  the  tapering  hole,  the 
impossibility  of  making  the  sections  of  a  crank-shaft  interchangeable. 
It  will  be  noted  that  the  analysis  assumes  the  shearing  stress  to  be 
distributed  uniformly  over  the  cross  section  of  the  bolt.  While 
this  assumption  has  sufficient  practical  accuracy,  the  stress  upon  the 
bolt-section  varies  in  intensity,  being  greatest  upon  that  side  of  the 
section  which  is  most  remote  from  the  centre  of  the  shaft. 

9.  STRESS  IN  CYLINDER-HEAD  STUDS.  —  The  stress  in  bolts  used 
in  securing  steam-cylinder  covers  and  in  other  joints  requiring  to 
be  tight  against  fluid  pressure,  is  affected  by  somewhat  complex 
conditions.  The  joint  may  be  made  metal  to  metal  and  ground 
or  a  gasket  may  be  interposed  between  the  flanges.  The  ma- 
terial of  the  latter  depends  upon  the  steam  pressure  and  the  cor- 
responding temperature.  Rubber  and  sheet  asbestos,  plain  or  in 
combination,  and  copper  in  corrugated  sheets,  wire,  or  wire-gauze, 
are  used  for  this  purpose. 


SCREW   FASTENINGS. 


93 


w 


The  bolts,  the  flanges,  and  the  gasket  (if  any),  are  all  more  or 
less  elastic.  The  bolts  are  set  up  with  an  initial  tension  which  is 
opposed  by  the  force  due  to  the  compression  of  the  flanges  and 
gasket.  Later,  steam  is  admitted  to  the  cylinder  placing  an  addi- 
tional tensile  load  upon  the  bolts, 
which  load  elongates  the  latter 
still  further  and  thus  reduces 
the  compressive  force,  as  above. 
Referring  to  Fig.  40,  let : 

St  =  initial  unit  stress  in  bolt ; 

Sc  =  initial  unit  force  on  bolt 
due  to  compression  of  gasket  and 
flanges. 

Then  :  S,  =  S . 

FIG.  40. 

When  the  steam  enters  the  cylin- 
der, the  forces  acting  unon  the  bolts  are  the  maximum  load,  W, 
due  to  the  steam  and  the  reduced  compressive  force  between  the 
flanges.     These  forces  are   opposed  by  the  tensile  stress  within 
the  bolt.     Let : 

Sw  =  unit  force  on  bolt  corresponding  with  external  load,  W\ 
Sc'  =  unit  force  on  bolt  corresponding  with  reduced  compres- 
sion between  flanges ; 
Stf  =  unit  tensile  stress  in  bolt  when  load,  W,  is  applied. 

Then  :  S/  =  Sw  +  Ser. 

If  the  bolt  stretches  by  an  amount  equal  to  the  initial  compres- 
sion of  the  other  members,  St'  =  Sv,  and  the  joint  will  open.  On 
the  other  hand,  with  a  short,  rigid  bolt,  connecting  ground  flanges 
without  gasket,  the  elongation  will  be  relatively  small  and,  with 
high  initial  stress,  the  value  of  St'  approaches  Sw,  plus  the  initial 
compressive  force,  Se.  In  any  event,  for  a  tight  joint,  the  intensity 
of  Stf  must  exceed  S^  and  Scf  must  be  greater  than  zero.  In 
Table  XXXI.,  there  are  given  the  numbers,  diameters,  working 
stresses,  and  ultimate  unit  strengths  of  the  cylinder-head  studs  for 
the  high-pressure  cylinders  of  some  of  the  later  vessels  of  the  U.  S. 
Navy.  The  area  under  load  includes  that  of  the  cylinder  and 
counterbore  plus,  in  some  cases,  a  portion  of  that  over  the  ports. 
When  a  cylinder  liner  is  used,  the  counterbore  may  be  only  ^ 
inch  deep. 


94 


MACHINE   DESIGN. 


TABLE  XXXI. 

STEEL  STUDS  FOR  CYLINDER  COVERS.     U.  S.  NAVY. 


H.  P.  Cylinder. 

Studs. 

Diameter, 
Ins. 

Initial  Press. 
Gauge,  Ibs. 
per  sq.  in. 

Total  Area 
Inside  of 
Flange, 

Total  Load 
at  Initial 
Press.,  Ibs. 

Number. 

Diameter. 

Stress  per 
sq.  in.  of 
Eff.  Area  at 
Initial 

Material  of 
Tensile 
Strength 
(Minimum) 

sq.  ins. 

Press.,  Ibs. 

Ibs.  per 
sq.  in. 

H 

250 

153 

38,250 

18 

: 

7036 

8o,OOO 

20* 

250 

342.25 

85,562 

28 

7240 

8o,OOO 

30 

200 

921.3 

184,260 

24 

I 

7264 

8o,000 

35 

250 

1484 

371,000 

38 

I 

7539 

75,000 

38* 

250         1      1720 

430,000 

38 

I 

7469 

75,000 

28.     Stresses  in  Nuts. 

i.  SHEARING,  RUPTURE,  AND  BEARING  PRESSURE  upon  the 
thread.  The  conditions  as  to  these  stresses  are  similar  to  those 
which  exist  with  the  bolt-thread,  excepting  that,  as  the  diameter 
at  the  root  of  the  nut-thread  is  the  nominal  diameter,  D,  plus  the 


clearance  spaces,  the  total  section  at  the  root  to  resist  shearing 
and  rupture  and  the  projected  area  of  the  thread  are  slightly 
greater  than  those  of  the  bolt. 

2.  BURSTING  STRESS.  —  In  Fig.  41,*  let: 
-    W=  axial  load  upon  the  bolt ; 

*  ' '  Report  of  Board  to  Recommend  a  Standard  Gauge  for  Bolts,  Nuts,  and  Screw- 
Threads,  U.  S.  Navy,"  May,  1 868. 


SCREW  FASTENINGS.  95 

N—  normal  pressure  upon  one  half  the  thread,  resolved  in  a 
direction  perpendicular  to  any  single  element  of  its  heli- 
coidal  surface  ; 

B  =  component  of  N  acting  in  a  direction  perpendicular  to  the 
axis  of  bolt  ; 

/5  =  base-angle  of  thread  ; 

<p  =  angle  of  repose  or  friction. 

Then,  without  friction  : 

W 


W=  27V  cos  B.:N 


-     —5 

2  COS  /?  ' 


W   sin  /?        W 
B  =  N  sin  /?  =  -  ---  ^  ==  —  -tan  /?. 

2       COS  ft  2 

Considering  friction,  the  true  direction  of  pressure,  R,  is  inclined 
to  the  normal,  N,  by  the  angle  <p  ;  and,  as  the  tendency  of  Wto 
resist  and  reverse  the  nut  is  opposed  by  the  friction,  the  bursting 
effect  of  W  will  be  reduced  and  the  angle  between  W  and  R  be- 
comes 3  —  (D.  Then  : 

W 
*-Ttan<0-f).  (65) 

In  the  Sellers  system  /?  =  30°.  Taking  fj.  =  tan  ^  =  0.124, 
<p  =  7°  04'  and  /9  —  ^  =  22°  56'.  Hence, 

W 
£=  —  tan  22°  56'  =0.2115  W7. 

A  given  axial  load,  W7,  produces,  then,  a  bursting  pressure,  B 
=  0.2  W;  and,  therefore,  the  vertical  section,  through  the  short 
diameter  of  the  nut  —  the  stress  upon  which  section  resists  B  — 
should  be  two  tenths  the  effective  bolt-area,  since  the  stress  upon 
the  latter  sustains  W. 

The  total  width  of  the  resisting  section  of  the  nut  is  dn  —  D, 
where  dn  =  short  diameter  of  nut  and  D  =  nominal  diameter  of 
bolt  ;  the  height  of  the  section  is  that,  ff=D,  of  the  nut.  For 
convenience,  assume  the  nominal  area  of  the  bolt  as  effective  in 
sustaining  W.  Then 

H(dn  -  D)  =  D(dn  -  U)  =  -  -D2  x  0.21  15, 
4 

.-.  d  =  i.i66D. 


96  MACHINE    DESIGN. 

Since,  in  this  system,  dn=  i.$D  -f  -J^  in.  for  finished  nuts,  there  is 
a  considerable  excess  of  strength  to  resist  bursting. 

29.     Efficiency  of  the  Screw. 

Consider  the  screw  with  regard  to  : 

i.  Loss  OF  POWER. —  The  efficiency  is  the  ratio  between  the 
useful  and  total  work.  Disregard  journal  friction,  as  absent  or 
uncertain. 

(a]  Square  Threads.  —  From  Fig.  36  and  equations  (50)  and 
(51),  we  have,  for  the  thread  only,  per  revolution,  in  raising  W 
with  friction  : 

Useful  Work      P0.7id0  W  ten  30~d0 

Total  Work  ~  P.xdQ  ~  ~W  tan  (<50  +  (f].^d^ 

(66) 
tan  o,, 

~  tan  (<50  +  p)  ~ 

which  expression  gives  the  efficiency,  E,  of  the  screw-thread  for 
any  given  pitch-angle,  d0,  of  the  mean  helix  and  any  angle  of  repose, 
(f.  When  the  screw  is  employed  solely  for  transmitting  power, 
the  pitch-angle  of  maximum  efficiency  should  be  used,  if  practi- 
cal considerations  do  not  prevent.  Differentiating  (66)  and  put- 
ting the  first  derivative  equal  to  zero  : 

dE       cot  (dn  +  v}  tan  3n 

:  o; 


whence  OQ  =  45°  —  <p  /  2,  which  value  of  30  will  make  E  a  maxi- 
mum. Substituting  in  (66)  : 

tan  (45°- f) 

E(max.}  = N— 

tan  I  45°  + 

If  ^  =  0.105,  <f>  =  6°,  o0  =  42°,  and  £=o.8i.  Good  practical 
reasons  make  it  undesirable  to  use  so  large  an  angle.  Multiple 
threaded  screws,  however,  owing  to  their  ample  bearing  surfaces, 
permit  relatively  steep  pitches. 

For  the  friction  of  the  support,  we  have,  for  a  screw  whose 
thrust-collar  has  a  mean  friction-diameter,  D' ,  a  work  of  collar- 
friction  per  revolution  equal  to  the  force  of  friction  multiplied  by 
its  circumferential  path  =  Wp'.nD'  =  W 'tan' <p* .xD1 '.  This  work 


SCREW   FASTENINGS. 


97 


must  be  added  to  that  expended  on  the  thread  in  order  to  find  the 
total  work.     Hence,  including  thread  and  collar-friction  : 


W  tan  (£0  +  <p)  xdQ  +  W  tan  <p'  . 


tan 


D' 


(67) 


Assuming  the  same  coefficient  of  friction  for  thread  and  collar, 
tan  <f>'  =  tan  <p  =  ft  and  E'  becomes  a  maximum  when 


cot 


>l 


D> 

I   +-y- 


In  the  table  relating  to  square-threaded  screws  which  follows, 
the  efficiencies  have  been  calculated,  but,  in  several  cases,  they 
have  been  checked  by  experiment  and  found  to  be  fair  average 
values.  The  efficiency  of  any  screw  will,  of  course,  vary  widely 
with  the  amount  of  lubrication.  The  same  coefficient  of  friction 
—  p=  0.15,  (f>  —  8° 30'  —  is  taken  for  both  thread  and  thrust- 
collar.  The  diameter  of  the  latter  is  assumed  to  be  that  of  the 
thread.  E  =  the  efficiency  per  cent,  when  there  is  no  friction  be- 
tween the  thrust-collar  and  its  bearing;  E'  =  the  efficiency  per 
cent,  allowing  for  thrust-collar  friction. 

TABLE  XXXIL* 
APPROXIMATE  EFFICIENCIES  OF  SQUARE  THREADED  SCREWS. 


Angle  of  Thread,  S0 

E 

^ 

2 

19 

ii 

3 

26 

14 

4 

32 

17 

5 

36 

21 

10 

55 

36 

20 

67 

48 

45°  -| 

79 

52 

The  efficiency  of  a  square-threaded  screw  in  lowering  IV  may 
be  found  from  the  values  of  the  useful  and  total  work  by  a  process 
similar  to  that  given  for  the  efficiency  in  raising  the  weight. 

*  Goodman  :  "  Mechanics  Applied  to  Engineering,"  1899,  p.  204. 


98  MACHINE   DESIGN. 

(&)  Triangular  Threads.  —  From  equation  (66),  we  have  for  the 
efficiency  of  a  square  thread  : 

tan  d0  +  tan  y 

Replacing  tan  <p  by  //  sec  /?,  we  have,  in  raising  W  with  friction 
in  triangular-threaded  screws,  for  the  thread  only,  the  efficiency  : 

*-*"*••  ItZ/*.T^?'         (68) 

For  the  friction  of  the  nut  on  its  washer  or  boss  —  assuming  the 
mean  friction  diameter  of  the  nut  as  %  of  D,  the  nominal  diameter 
of  the  bolt  —  we  have  a  work  of  nut-friction  per  revolution  of 
£Ftan  <pr  •  %xD,  which  work  must  be  added  to  that  expended  on 
the  thread.  Hence,  including  thread  and  nut  friction,  as  in  (67)  : 

Wtan30.iui0 


J0  -f  <p)xdQ  +  W  tan  <p  '  • 

tan  fi 

(69) 


0  "*:        Y  +  4./%.tan  »'. 
i  —  tan  ^0  tan  y      * 

Replacing  tan  <p  by  fi  sec  /9  and  tan  <p'  by  // ' : 

tan  3n 


£'  = 


0 


tan 


In  the  Sellers  system,  sec  /?  =  1.15.      Hence  : 


tan  d0  +  1.15  ft        ^ 


(7.) 


tan 


The  efficiency  of  a  triangular-threaded  screw  in  lowering  W  may 
be  found  by  a  similar  process. 

Mr.  Wilfred  Lewis  gives  the  following  approximate  formulae 
for  the  external  force  and  efficiency  of  triangular-threaded  screws, 
which  formulae  he  states  are  applicable  with  a  close  degree  of  ac- 
curacy to  most  of  the  cases  which  occur  in  practice.  Let : 


SCREW   FASTENINGS.  99 

p  =  pitch  of  screw  ; 

D  =  outside  diameter  of  screw  ; 

P=  force  applied  at  circumference  (of  screw)  to  lift  a  unit  of 

weight ; 
E'  =  efficiency  of  screw  in  lifting. 

Then:  P  =  f-±^    and     E'  - ^  (72) 

Experiments,*  conducted  by  Mr.  James  McBride  to  deter- 
mine the  efficiency  of  a  screw,  gave  results  in  accord  with 
the  formulae  given  above.  The  test  was  made  with  an  ordinary 
2-inch  screw-bolt,  not  especially  prepared.  The  thread  was  of  the 
standard  V-shape  and  of  0.2 2 -inch  pitch.  The  nut  was  not  faced 
and  had  the  flat  side  to  the  washer,  the  latter  being  of  malleable 
iron,  not  faced.  The  contact-surfaces  of  nut  and  washer  and  the 
threads  of  nut  and  bolt  were  well  lubricated  with  lard  oil.  The 
axial,  tensile  load  upon  the  bolt  was  7,500  Ibs.  The  nut  was  a 
good  fit,  and,  when  not  loaded,  was  easily  run  up  and  down  the 
bolt  with  the  fingers.  Wrenches  of  different  lengths  were  applied 
to  the  nut  and  a  known  force  which  would  just  move  the  latter, 
exerted  upon  each  wrench.  The  ratio  between  the  useful  work  of 
lifting  the  weight  and  the  total  work  expended  upon  the  nut,  gave 
the  efficiency,  which,  for  5  tests,  averaged  10.19  per  cent. 

The  effective  diameter  of  a  2-inch  bolt  =  1.712  in.  The  mean 
thread  diameter,  d^  is  therefore  1.856  in.  The  pitch  =  0.2222  in. 
and  tan  30  =  pfxd^  =  0.038  in.  Assuming  //  =  o.  1 5  and  //'  =  o.  10, 
and  substituting  in  formula  (71),  we  find  E'  =  10.7  per  cent. 
Again,  substituting  the  values  of  /  and  D  in  formula  (72),  we 
find  E'  =  10  per  cent.  The  theoretical  and  experimental  results 
are  hence  practically  the  same. 

2.  Loss  OF  AXIAL  STRENGTH.  —  In  screwing  up  a  nut,  the  bolt 
is  subjected  to  the  tensile  or  compressive  stress  corresponding  with 
the  axial  load  produced  and  to  the  torsional  stress  developed 
through  the  action  of  the  nut-thread  on  the  bolt-thread.  The 
torsional  action  results  from  thread-friction  and  from  that  com- 
ponent of  the  axial  load  which  must  be  overcome  in  order  to  move 
the  latter  up  the  inclined  plane  of  the  screw. 

The  measure  of  torsion  is  the  twisting  moment,  T.M.,  the  latter 
being  the  product  of  the  force,  P,  Fig.  36,  by  its  lever-arm  dQJ2 

*  Trans.  Am.  Soc.  Meek.  Engrs.,  Vol.  XII. 


100  MACHINE    DESIGN. 

=  /.  For  equilibrium,  the  twisting  moment  must  be  equal  to  the 
resisting  moment.  The  latter,  for  a  circular  section,  is  the  product 
of  the  unit  shearing  stress  Sa,  at  the  periphery  of  the  section  by 
the  polar  modulus  of  the  section,  which  is  /r^3/i6,  where  d  is  the 
diameter.  Taking,  for  convenience,  dQ  —  dt  we  have  /  =  dJ2  and  : 

TM.-Pt-S.~.-.P-S.~,  (73) 

i.  e.,  if  St  be  the  greatest  allowable  shearing  stress  in  all  bolts,  the 
turning  force  P,  which  may  be  applied  as  above  with  safety,  varies 
as  the  square  of  the  diameter.  This  condition  prevails  also  with 
the  axial  load,  since  that  load  by  (60)  is 


in  which  St  is  the  greatest  allowable  tensile  unit  stress. 

The  relation  between  the  twisting  force  and  the  axial  load  is 
given  by  (51)  as  : 

P 


<p  is  here  a  constant  for  all  screws  under  similar  conditions  of  sur- 
face and  lubrication.  The  angle,  30,  is,  however,  in  the  Sellers 
system,  variable,  being  a  maximum  at  the  smallest  diameter.  For 
example,  it  is  4°  11'  for  the  ^-inch  screw  and  i°  45'  for  the  3- 
inch  screw.  Replacing  IV  in  (51)  by  its  equivalent  : 

P-S,~.ton(39  +  <p), 

in  which  <p  may  be  regarded  as  simply  a  constant  addition  to  d0. 
It  will  be  seen  that,  while  P  produces  a  shearing  stress  which  varies 
as  dz,  it  develops  a  tensile  stress  varying  not  only  as  d2  but  also 
as  tan  (dQ  -f  <p).  Since  tan  d0  increases  with  decreased  diameter,  it 
is  evident  that,  with  the  same  tensile  stress  in  two  bolts  of  different 
diameters,  the  shearing  stress  will  be  larger  in  the  smaller  bolt. 

The  disadvantage  of  this  increased  shearing  stress  in  setting  up 
the  nuts  of  small  bolts,  is  aggravated  by  the  tendency  of  the  aver- 
age mechanic  to  put  excessive  force  upon  the  wrench  in  such  cases. 
As  a  result  of  a  series  of  tests  made  at  Cornell  University,  Pro- 
fessor Barr  *  concludes  : 

"  (a)  That  the  initial  tensile  load  due  to  screwing  up  for  a  tight  joint  varies  about  as 
the  diameter  of  the  bolt  —  that  is,  a  mechanic  will  graduate  the  pull  on  the  wrench  in 

*  "Notes  on  Machine  Design,"  1900,  p.  106. 


SCREW   FASTENINGS.  IOI 

about  that  ratio,  (b)  That  the  load  produced  maybe  estimated  at  16,000  Ibs.  per 
inch  of  diameter  of  bolt,  or 

P^  =  16,000  d, 

in  which  Pl  is  the  initial  load  in  pounds  due  to  screwing  up,  and  d  is  the  nominal  (out- 
side) diameter  of  the  screw  thread.  *  *  *  If  the  initial  load  due  to  screwing  up  be 
divided  by  the  cross-sectional  area  of  the  bolt  at  the  bottom  of  the  thread,  the  initial  in- 
tensity of  the  tensile  stress  is  obtained.  The  above  experiments  indicate  that  this  in- 
tensity of  stress  varies,  approximately,  inversely  as  the  nominal  diameter  (d}  of  the 
bolt  ;  and  that  it  may  frequently  equal  or  exceed  : 

30,000 
/=       d      Ibs.  per  sq.  in. 

In  addition  to  this  tensile  stress,  there  is  a  considerable  twisting  action  on  the  bolt." 

Mr.  Harvey  D.  Williams  *  has  calculated  the  efficiency  of  the 
U.  S.  Standard  bolts  whose  proportions  are  given  in  Table  XL, 
on  the  basis  of  the  ratio  between  the  useful  fibre  stress  —  or  that 
portion  which  would  be  required  for  the  support  of  the  safe  axial 
load  only  —  and  the  total  fibre  stress  produced  in  screwing  up  the 
nut.  His  results  are  given  in  Table  XXXIII. 

The  method  of  computing  the  efficiencies  given,  is  as 
follows  : 

From  (55)  the  value  of  Pis  found  in  terms  of  W,  p  and  dQ  be- 
ing known  for  any  given  bolt  and  /j.  being  taken  as  0.15.  Then, 
P=  K'W,  where  A'  is  a  numerical  factor.  Also  : 

Twisting  Moment  =  T.M.  =  P  x  -£  ; 
from  (7  3):  \6T.M. 


from  (60): 

S<=^2' 

Then  :  _ 

Maximum  tensile  stress  =  f=  |  St  +  \\/S?  +  4$*  ;  f          (74) 

w 


But,  to  support  the  load,  W,  there  is  required  only  per  sq.  in.  the 

A.W 

Useful  tensile  stress  =f'  =  St  =  —-& 
The   load,    W,  must  be   reduced  below  the  amount  which   the 

*Jour.  Am.  Soc.  Naval  Engineers,  Vol.  XIII.,  No.  2. 
t  Lanza:   "Applied  Mechanics,"   1897,  p.  892. 


102  MACHINE    DESIGN. 

screw  would  carry,  if  under  direct  tension  only,  in  order  that  the 
load  produced  by  the  stress,/,  shall  not  exceed  the  strength  of 
the  bolt.  Hence,  in  this  respect  —  considering  the  thread-friction 
only  —  the  efficiency  of  the  bolt  in  raising  the  weight  W,  is  : 


in  which  W  is  the  useful  axial  load  in  pounds,  T.  M.  is  the  torque 
in  inch-pounds,  and  d  is  the  effective  diameter  in  inches.     Equa- 
tion (74)  is  similar  to  (62),  the  former  being  the  formula  deduced 
by  Grashof  and  the  latter  that  by  Rankine. 
Referring  to  the  table,  Mr.  Williams  says  : 

"The  factor  of  safety  equals  the  direct  load  factor  7,  divided  by  the  efficiency; 
and  the  safe  loads  given  in  the  body  of  the  table  correspond  to  the  factor  of  safety 
in  the  same  horizontal  line  and  the  ultimate  strength  at  the  head  of  the  column.  To 
facilitate  the  computation  of  bolts  having  threads  which  are  finer  or  coarser  than  the 
standard,  the  column  headed  "Relative  Fineness  of  Thread"  is  given,  in  explana- 
tion of  which  it  need  only  be  remarked  that  the  relative  fineness  of  thread  equals  the 
number  of  threads  per  inch  multiplied  by  the  diameter  and  that  bolts  of  different 
sizes  but  having  the  same  relative  fineness  of  thread  will  have  the  same  efficiency  and 
the  same  factor  of  safety.  As  the  thread  is  made  relatively  finer  and  finer  beyond  the 
limits  of  the  table,  the  corresponding  efficiency  approaches  88.06  per  cent,  as  a  limiting 
value,  beyond  which  it  cannot  go.  The  factor  of  safety  meantime  approaches  the  limit- 
ing value,  7.95.  The  efficiency  of  a  hollow  bolt  is  always  greater  than  that  of  a  solid 
bolt  of  the  same  diameter  and  number  of  threads,  the  limiting  efficiency  for  a  very  fine 
thread  on  a  very  thin  tube  being  96.48  per  cent.,  as  against  88.06  per  cent,  for  a  solid 
bolt.  The  error  will  therefore  be  always  on  the  safe  side,  if  we  use  the  efficiencies  and 
factors  of  safety  given  in  the  table  in  computing  hollow  bolts.  '  ' 

Seaton  and  Rounthwaite  *  give  a  table  for  the  effective  strength 
of  Whitworth  screws  in  which  the  torsional  stress  is  allowed  for 
by  assuming  progressively  lower  values  for  the  working  stress  as 
the  bolts  diminish  in  size.  The  table  is  based  on  the  relation  : 

Working  Stress  per  sq.  in.  =  (Effective  Area)&  x  C, 

where  C  =  5,000  for  iron  or  mild  steel  and  1,000  for  muntz  or 
gun-metal.  For  iron  or  steel  bolts  above  2  inches  in  diameter 
and  gun-metal  or  bronze  ones  above  3^  -inch  diameter,  the 
moment  of  the  twisting  stress  is  small,  proportionately,  and  is 
neglected  in  the  table,  the  working  stresses  in  Ibs.  per  sq.  in., 
for  all  sizes  above  those  noted  being  uniformly  7,000  and  2,500, 
respectively. 

*  "Pocketbook  of  Marine  Engineering  Rules  and  Tables,"  1899,  p.  73. 


SCREW    FASTENINGS. 


I03 


TABLE  XXXIII. 
SAFE  LOADS  FOR  U.  S.  STANDARD  BOLTS. 


Ultimate  Strength. 

•o 

i 

£ 

20,000 

40,000 

50,000 

6O,OOO 

65,000 

80,000 

95,000 

8 

•S 

c 

S. 

dt 

"o 

M 
"8 

S 

I 

•s 

1 

1 

| 

E 

1 

Q 

c 

p 

1 

Efficiency. 

7 

1 

1 

Is 

22 

B  Bolt  Mat. 

A  Bolt  Mat. 

G       Q 

if 

Grade  Mac! 
gings 

1 

1 

zL 

? 
f 

Cu,  8$$ 

I 

Is 

0 

I 
U 

jl 

S 

5 

\ 

20 

74.68 

9-4 

57 

115 

143 

172 

186 

229 

272 

A 

18 

76.56  9-1 

99 

198 

247 

297 

322 

396 

470 

6 

1 

16 

77-49 

Q 

150 

301 

376 

451 

488 

601 

A 

14 

78.38 

8.9 

207 

415 

519 

623 

675 

830 

986 

6.5 

F 

13 

78.48 

8.9 

282 

564 

704 

845 

915 

1,125 

1,340 

12 

78.92 

8.9 

365 

730 

912 

1,095 

1,186 

1,460 

1,730 

i 

II 

79.11 

8.8 

456 

1,140 

1,370 

1,480 

1,820 

2,170 

7-5 

I 

10 

80.00 

8.8 

690 

1,380 

1,725 

2,070 

2,240 

2,760 

3,280 

£ 

Q 

80.48  8.7 

964 

I,93° 

2,410 

2,900 

3,!40 

3,86o 

4,580 

8 

8 

80.61  8.7 

1,265 

2,530 

3,i7o 

3,800 

4,120 

5,060 

6,010 

7 

80.48  8.7 

i,595 

3,190 

3,990 

4,790 

5,180 

6,380 

7,570 

7 

81.37  8.6 

2,070 

4,140 

5,180 

6,210 

6,73° 

8,280 

9,830 

6 

80.92  8.7 

2,440 

4,890       6,110 

7,330 

7,940 

9,780 

n,  600 

9 

6 

8i.6i!8.6 

3,020 

6,040 

7,540 

9,060 

9,800 

12,050 

14,300 

5^ 

81.56  8.6 

3,530 

7,060 

8,820 

10,600 

11,500 

14,100 

16,75° 

5 

81.37;  8.6 

4,060 

8,120 

10,150 

12,200 

13,200 

16,200 

19,250 

5 

81.92  8.5    4,800 

9,600 

12,000 

14,400 

15,600 

19,200     22,800 

9 

, 

Ji 

81.61  8.6 
82.43  8.5 

5,360 

7,120 

10,750 
14,200 

13,400 
17,800 

16,100 
21,400 

I7,4oo 
23,100 

21,500 
28,500 

25,500 
33,8oo 

10 

.] 

4 

82.351  8.5 

8,750 

17,500 

21,900 

26,300 

28,400 

35,ooo 

41,500 

II 

•| 

4 

83.20  8.4  11,000 

22,000 

27,50° 

33,000 

35,7oo 

44,000 

52,200 

12 

3 

4 

83.42:8.413,400 

26,800 

33,5oo 

40,200 

43,600 

53,6oo 

63,600 

13 

4 

83.8818.316,100 

32,200 

4o,2ooj     48,400 

52,400 

64,400 

76,400 

14 

3i 

4 

84.20 

8.319,000 

38,100 

47,600 

57,2oo 

61,900 

76,200 

90,400 

15 

3f 

4 

84.47 

8.3:22,200 

44,500 

55,600 

66,700 

72,300 

89,000 

105,500 

16 

4 

4 

84.71 

8.325,700 

51,400 

64,200 

77,000 

83,400 

102,800 

122,000 

17 
18 

4\ 
4f 

4 
4 

84.91  8.2  29,350 
85.09  8.2  33,300 

58,700 
66,600 

73,400 
83,200 

88,100 
100,000 

95,4oo 
108,000 

117,400 
133,000 

139,300 
158,000 

19 

20 

41 

5 

4 
4 

85.26'  8.2  37,400 
85.44  8.2  41,900 

75,ooo 
83,800 

93,700 

105,000 

112,000 
126,000 

122,000 
136,000 

150,000 
167,500 

178,000 
199,000 

21 

5-V 

4 

85.55  8.2  46,600 

93,2oo 

116,500 

I4O,OOO 

151,000 

186,000 

221,000 

22 

5j 

4 

85.68;  8.2  51,500 

103,000 

129,000 

154,500 

167,000 

206,000 

244,500 

23 

sl 

4 

85.8o!  8.2  56,700 

113,500 

142,000 

170,000 

l84,000 

227,000 

269,000 

24 

6 

4 

85.92    8.1:62,000 

124,000 

155,000 

186,000 

202,000 

248,000 

295,000 

30.     Types  of  Screw  Fastenings. 

Screw  fastenings  have  forms  as  numerous  as  their  uses  are 
varied.  Brief  reference  will  be  made  to  a  few  types. 

I.  BOLTS,  TAP  BOLTS,  STUDS. — The  proportions  of  Machine 
Bolts  have  been  given  in  preceding  tables.  When  employed  to 


104 


MACHINE   DESIGN. 


FIG.  42. 


join  flanges,  as  in  Fig.  40,  this  form,  if  short  and  tightly  fitted, 
gives  a  most  rigid  connection.  For  steam  cylinder  heads,  they 
are  somewhat  objectionable,  since,  if  a  bolt  breaks,  the  lagging 
must  be  removed  to  replace  it. 

With  the  Stud,  on  the  contrary,  the  broken 
part    may  be    drilled    out    readily  from    the 
flange.     The  stud  has  further  advantages  in 
its  use  when  through  bolts  are  inadmissible 
and  in  the  fact  that,  once  set  in  the  weak 
threads  of  cast  metal,  it  need  not  be  removed, 
as  the  tap-bolt    must  be,  to   disconnect   the 
parts.     The    threaded  portion  which   enters 
the    casting  should  be  longer  than  that  for 
the  nut  and  the   unthreaded  shank  should  be  shorter  than  the 
flange  through  which  it  passes.     Fig.  42  *  gives   good  general 
oroportions,  as  follows  : 
D  =  diameter  of  stud  ; 
F=  \.2$D  =  depth  of  hole  ; 
G  •=  i .  1 5/?  =  length  of  stud  to  be  screwed  in  ; 
H  =  1.30/2  =  length  of  thread  on  nut-end  ; 
J  =  F  =  length  of  thread  on  opposite  end. 
The  Tap-Bolt,  Fig.  43,  is  practically  a  machine-bolt  without  a 
nut,  the  shank  passing  through  a  flange  or  other  member  and  the 
threaded    section    screwing    into  the   remaining    part    connected. 
Like  the  stud,  it  is  liable  to  stick  fast  and  it  has 
the  further  disadvantage  that  its  frequent  removal 
to  break  the  joint  will  wear  the  weak  threads  of 
a  casting.     For  this  reason,  the  depth  of  the  tapped 
hole   should  be  from   1.5  to  twice  the  diameter. 
The  proportions  of  counter-sunk  and  round  and 
button-head  tap-bolts    and    screws    are    given    in 
Table  XXXIV. 

2.  SET-SCREWS  are  fastenings  which  are  suit- 
able only  for  light  work.  They  find  most  fre- 
quent use  in  securing  pulleys,  etc.,  to  shafting. 
Their  chief  advantage  is  that  no  key-way  is  necessary  and  that, 
therefore,  the  connected  piece  may  be  readily  shifted.  The 
disadvantages  are  the  liability  to  slip,  the  burring  of  the  shaft, 

*  American  Machinist,  June  6,  1901. 


FIG.    43- 


SCREW   FASTENINGS. 


ICK 


TABLE  XXXIV. 

TAP-BOLTS  AND  SET-SCREWS. 

(NEWPORT  NEWS  SHIPBUILDING  AND  DRY  DOCK  Co.) 

Suit  on  Head  Scrntf 

Ji 


HeaJles*  &t  tScrmt 


Tap  Bolts. 


Round  Heads.  Button  Heads. 


meter 
B 


Diameter 
B 


Depth  of 
Head,C 


the  radial  stress  in  the  hub,  and  the  uneven  bearing  and  slight 
eccentricity  of  the  latter,  if  a  free  fit.  The  points  of  set-screws 
are  made  flat,  conical,  rounded,  or  cupped.  A  shallow  hole  is 
sometimes  bored  in  the  shaft  to  receive  the  point.  In  light  work, 
however,  the  screw  is  set  up  sufficiently  to  make  its  own  indenta- 
tion. A  relatively  strong  fastening  may  be  made  by  interposing  a 
thin  steel  plate  between  the  set-screw  and  a  "  flat "  filed  on  the 
shaft,  the  plate  fitting  into  a  recess  in  the  hub. 

Professor  Lanza  *  tested  the  holding  power  of  points  of  various 
forms  upon  a  ^|-in.  shaft,  the  screws  being  of  wrought  iron,  f -in. 
diameter,  10  threads  to  the  inch,  and  set  up  with  a  force  of  75 

*  Trans.  Am.  Soc.  Mech.  Engs.,  Vol.   X. 


106  MACHINE    DESIGN. 

Ibs.  at  the  end  of  a  lo-in.  monkey  wrench.  The  shaft  was  of  steel 
and  the  points  made  but  little  impression  upon  it.  Two  screws 
were  used  to  secure  a  pulley  to  the  shaft  and  then  the  circum- 
ferential load  required  to  make  the  pulley  slip  was  found,  from 
which  load  the  resistance  of  the  screws  was  determined.  The 
shapes  of  the  points  were  : 

A.  Ends  perfectly  flat,  T9^  in.  diameter. 

B.  Ends  rounded,  radius  \  in. 

C.  Ends  rounded,  radius  \  in. 

D.  Ends  cup-shaped  and  case-hardened. 
The  holding  power  in  pounds  was  : 

Lowest.  Highest.  Average. 

A.  1412  2294  2064 

B.  2747  3079  2912 

C.  1902  3079  2573 

D.  1962  2958  2470 

Professor  Lanza  states  as  to  : 

A.  The  set-screws  were  not  entirely  normal  to  the  shaft ;  hence  they  bore  less  in 
the  earlier  trials  before  they  had  become  flattened  by  wear. 

B.  The  ends  of  these  set-screws,  after  the  first  two  trials,  were  found  to  be  flattened, 
the  flattened  area  having  a  diameter  of  about  \  in. 

f.  The  ends  were  found,  after  the  first  two  trials,  to  be  flattened,  as  in  B. 

D.  The  first  test  held  well  because  the  edges  were  sharp  ;  then  the  holding  power 
fell  off  till  they  had  become  flattened  in  a  manner  similar  to  £,  when  the  holding  power 
increased  again. 

3.  EYE-BOLTS.  —  Good  proportions  for  eye -bolts  are  given  in 
Table  XXXV.     Since  the  bolt  when  screwed  home  is  without 
load,  the  torsional  effect  is  negligible  and  the  same  working  stress 

may  be  used  for  all  sizes.  Owing 
to  bending  action,  the  sides  of  the 
eye  are  subjected  to  greater  stress 
than  the  body  of  the  bolt,  and 
their  combined  cross-sectional  area 

is  made  greater  than   that  of  the 
FIG.  44. 

weakest  section  at   G,  the  excess 

being  about  200  per  cent,  in  the  |-inch  bolt  and  decreasing  rap- 
idly with  the  larger  sizes. 

4.  STAY-BOLTS. — These  bolts  are  used  to  brace  the  flat  sur- 
faces of  boilers.     They  vary  in  details  of  form  and  manufacture. 
Good  practice  is  shown  by  Fig.  44.     The  bolt  is  threaded  at  each 
end,  turned  down  in  the  shank  to  the  diameter  at  the  base  of  the 
thread,  screwed  into  both  sheets,  and  riveted  over  cold  with  shallow 
spherical   heads.      Minimum   general  proportions  are :    diameter, 


SCREW   FASTENINGS. 


lO/ 


TABLE  XXXV. 

EYE-BOLTS. 
(UNION  IRON  WORKS.) 


Capacity  Based  on  10,000  Ibs. 
per  sq.  Inch  Strain. 


767 
1,104 
I>963 
2,485 
3.712 
5,135 
6,903 
7,854 
9,940 
12,270 
13,520 

16,210 

19,150 
22,340 


-|  inch  ;  threads  per  inch,  1 2  ;  spacing,  centre  to  centre,  4  inches. 
The  stress  at  root  of  thread  should  not  exceed  6,000  Ibs.  per 
sq.  in.  A  "  detector  "  hole — at  which  leakage  will  show  when  the 
bolt  is  broken — is  drilled  or  punched,  preferably  the  former,  from 
the  outer  end  of  the  bolt  inward  to  the  beginning  of  the  shank. 

Flexibility  is  a  most  important  requirement  of  these  bolts.  In 
some  cases,  various  combinations  of  the  ball-and-socket  joint  have 
been  applied  at  one  end.  In  the  ordinary  type,  this  quality  de- 
pends upon  the  material,  the  reduced  shank,  and  the  form  and 
method  of  driving  the  heads.  As  material,  the  best  grade  of 
wrought  iron  is  preferred. 

The  Falls  Hollow  Staybolt  is  rolled  with  a  central  hole  through- 
out, thus  avoiding  later  drilling  or  punching.  The  bolt  is  also 
threaded  through  its  full  length  with,  therefore,  uniform  strength  at 
all  points.  The  size  of  the  hole  is  usually  -|  inch  or  y3^  inch.  It 
serves  not  only  as  a  "  detector  "  but  also,  if  desired,  as  an  inlet  for 
the  admission  of  air  to  aid  combustion. 

The  data  and  results  of  tests  of  these  bolts  at  McGill  University  are  : 


io8 


MACHINE   DESIGN. 


Material,  double-refined  charcoal  stay-bolt  iron,  i  inch  diameter, 
•j3g  inch  hole;  length,  25^  inch  ;  mean  diameter,  outside,  1.014 
inch  ;  yield-point,  32,000  Ibs.  per  sq.  in.  ;  ultimate  tensile  strength, 
49,300  Ibs.  per  sq.  in.;  equivalent  elongation  in  8  inches, 
per  cent.  ;  reduction  of  area,  45.7  per  cent. 

Chief  Engineers  Sprague  and  Tower,  U.  S.  Navy,  in  1879, 
exhaustive  experiments  upon  the  strength  of  boiler-bracing.  From 
their  report  *  the  following  data  are  taken  with  regard  to  the  re- 
sistance of  screw  stay-bolts  in  flat  surfaces  : 

"In  reference  to  iron  and  low  steel  bolts,  andiron  and  low  steel  plates,  and  copper 
plates  and  iron  bolts,  after  a  careful  examination  of  the  results  of  these  experiments  in 
particular,  we  are  satisfied  that  the  following  formulae  will  correctly  and  safely  repre- 
sent the  working  strength  of  good  material  in  flat  surfaces,  supported  by  screw  stay-bolts 
with  riveted  button-shaped  heads  or  with  nuts,  when  the  thickness  of  the  plates  forming 
said  surfaces  and  the  screw  stay-bolts  are  made  in  accordance  with  the  dimensions  and 
conditions  given  in  Table  Y.  W=  safe-working  pressure  ;  T=  thickness  of  plate  ; 
*/=  distance  from  centre  to  centre  of  stay-bolt : 

T2 
For  iron  plates  and  iron  bolts W=  24000  — 

Tl 
For  low  steel  plates  and  iron  bolts W—  25000  — 


For  low  steel  plates  and  low  steel  bolts. 
For  iron  plates  and  iron  bolts,  with  nuts 


'=28°°°£ 

'=  40000  Z? 


For  copper  plates  and  iron  bolts 


=  14500 


"  To  obtain  the  ultimate  bursting  pressure,  multiply  the  results  of  the  above  formulae 
by  8,  which  is  the  factor  of  safety  used. 

TABLE  Y. 

DIMENSIONS  AND  CONDITIONS  FOR  MAKING  IRON  AND  Low  STEEL   SCREW  STAY- 
BOLTS  FOR  FLAT  SURFACES  SUBJECT  TO  INTERNAL  PRESSURE  FOR  DIS- 
TANCES RANGING  FROM  FOUR  TO  EIGHT  INCHES  (INCLUSIVE) 
FROM  CENTRE  TO  CENTRE  OF  STAY-BOLT. 


Nuts. 


ills  m    5 

(««     155   ;  K 


*"  Experiments  in  Boiler  Bracing,"  U.  S.  Navy  Dep't,  1879. 


SCREW   FASTENINGS. 


I09 


"  The  rivet-heads  to  be  a  segment  of  a  sphere,  formed  by  first  upsetting  the  end  of  the 
bolt  with  a  few  quick,  sharp  blows  of  the  hammer,  then  finished  to  shape  with  the  ham- 
mer and  button-head  set.  Where  nuts  can  be  used  instead  of  riveted  heads,  they  should 
be  of  the  standard  size,  suited  to  trie  diameter  of  the  bolt,  faced  on  the  side  bearing  on 
the  plate,  and  dished  out  so  as  to  form  an  annular  bearing  surface  of  as  large  a  diameter 
as  the  nut  will  allow,  aud  of  a  breadth  and  depth  given  in  the  table.  Before  securing 
the  nut  in  place  the  dished  portion  should  be  filled  with  red-lead  putty  made  stiff  with 
fine  iron  borings." 

The  regulations  (January,  1901)  of  the  U.  S.  Board  of  Supervis- 
ing Inspectors  of  Steam  Vessels,  prescribe  for  plates,  ^  inch  thick 
and  under,  used  in  boilers  as  "  flat  surfaces  fitted  with  screw  stay- 
bolts  riveted  over,  screw  stay-bolts  and  nuts,  or  plain  bolt  with 
single  nut  and  socket,  or  riveted  head  and  socket,"  a  working 
pressure  determined  by  the  formula  : 

*-*£.  04 

where  P  =.  working  pressure  in  Ibs.,  C  —  112,  /  =  number  of  six- 
teenths in  plate  thickness  (i.  e.,  for  -j^-inch  plate,  /=  7),  and  d  = 
distance  between  stays  in  inches.  For  plates  above  -j^-inch  thick 
C '  =  1 20.  The  pressures,  as  above,  refer  to  fire-box  plates.  Also, 


FIG.  45- 

"  on  other  flat  surfaces  there  may  be  used  stay-bolts  with  ends 
threaded,  having  nuts  on  same,  both  on  the  outside  and  inside  of 
plates."  For  these  surfaces,  formula  (76)  is  used  with  C  =  140. 
5..  ARMOR  BOLTS. — The  proportions  of  threads  for  these  bolts, 
as  used  in  the  U.  S.  Navy,  have  been  given  in  §  24.  The  method 
of  their  application  with  side,  diagonal,  and  belt-armor,  is  illustrated 
in  Fig.  45.  The  armor-plate  is  fitted  snugly  to  a  backing  of  teak, 
the  latter  being  secured  to  the  backing  plates  of  the  hull  by  bolts 
countersunk  in  the  wood.  After  the  armor-bolt  is  screwed  down 


no 


MACHINE   DESIGN. 


to  a  bearing  in  the  plate,  the  space  around  the  shank  is  calked 
solidly  with  oakum  and  the  nut  is  screwed  up  against  a  lead 
washer  until  it  embeds  itself  in  the  latter,  thus  causing  the  lead  to 
flow  into  the  thread.  As  an  additional  precaution  against  leakage, 
the  backing  plates  and  washer  are  coated  with  red  lead,  all  inter- 
stices in  the  backing  are  filled  with  red  lead  under  pressure,  and 
the  joint  between  the  backing  plates  is  calked.  Turret-armor  is 
secured  by  similar  bolts  which  have,  however,  a  solid  head  instead 
of  a  nut.  The  spacing,  in  all  cases,  is  such  as  to  provide  one  bolt 
for  each  5  sq.  ft.  of  armor  surface. 


3i.     Methods  of  Manufacture. 
Bolts  are  headed  hot  from  round  stock  ;  then  threaded  and 

pointed.     Nuts  are  pressed  or  forged  hot,  or  pressed  and  punched 

cold,  and  tapped. 

i.  BOLT-BLANKS. — The  round  stock  is  sheared  into  lengths 

containing  enough  material  for  shank  and  head.      Each  blank  is 

then  heated  and  the  head 
formed  in  a  forging  ma- 
chine. Figs.  46  and  460. 
give  a  view,  plan,  and 
details  of  the  I  3^ -inch 
Heading  and  Forging 
Machine  built  by  the 
Acme  Machinery  Co., 
Cleveland,  O.,  and  illus- 
trated herein  through 


the    courtesy    of    that 
FIG.  46.  company. 

"  There  are  two  sets  of  tools  :  the  stationary  or  gripping  dies,  A,  which  hold  and  re- 
lease the  blank  and  the  heading  die,  B,  and  finishing  punch,  C,  which  form  the  head 
and  are  carried  by  a  tool-holder  fixed  to  a  reciprocating  plunger.  The  latter  is  driven 
from  the  shaft  which  is  actuated  by  a  fly-wheel  with  clutch-connection  controlled  by  a 
pedal.  The  plunging  or  upsetting  mechanism  is  omitted  from  the  plan  ;  it  moves  on 
the  line  marked  "centre  of  heading  slide." 

"The  dies,  A,  are  divided  and  open  vertically  on  the  centre-line  of  the  lower  cylin- 
drical groove,  Z>,  and  the  upper  groove,  E,  also  cylindrical  but  having  a  square  or 
hexagonal  recess  for  the  bolt-head.  The  opening  and  closing  of  the  dies  is  done  by  the 
toggle-joint  mechanism  shown.  The  latter  is  operated,  through  an  intervening  spring, 
by  an  adjustable  connecting  rod  driven  from  the  shaft.  The  bolt-blank  is  upset  while 
in  groove,  Z>,  by  the  heading  die,  B.  It  is  then  shifted  to  E  where  the  head  is  finished 
by  punch,  C.  The  grooves,  D  and  E,  are  concentric  respectively  with  die,  B,  and 


SCREW   FASTENINGS. 


I  I  I 


punch,  C.  The  latter  die  holds  a  die-plug  and  the  punch  has  a  head,  both  suitably 
shaped  for  upsetting  square,  or  with  other  forms,  hexagonal  heads. 

"  In  forging  a  bolt-head,  the  operator  places  a  heated  blank  in  groove,  D,  and  touches 
the  pedal.  The  machine  makes  a  "plunge"  and  the  gripping  dies  close,  remaining 
thus  while  die,  £,  advances  and  forms  the  head  and  until  the  plunger  has  travelled 
about  3  inches.  When  the  machine  has  passed  its  forward  centre,  the  plunger  has  re- 
ceded about  $£  inch  and  the  gripping  dies  open.  The  operator  now  removes  the  bolt 
to  the  upper  groove,  E,  and  again  touches  the  pedal,  upon  which  the  finishing  punch 
enters  the  die  at  E,  presses  against  the  head,  and  removes  the  slight  draught  formed 
during  the  first  stroke.  At  the  same  time,  the  side  pressure  of  the  dies  drives  all  '  fins ' 
back  into  the  head.  The  bolt  is  really  made  during  the  first  stroke,  while  the  heated 
metal  is  at  its  best  for  working.  The  second  stroke  simply  removes  the  slight  taper  of 
the  head  and  smooths  the  sides  of  the  latter. 

"  The  toggle-joint  gives  maximum  pressure  when  the  gripping  dies  are  closed.  Until 
its  joints  are  in  line,  it  is  acted  upon  by  an  elastic  force  in  the  spring,  so  that  if  the  dies 
become  obstructed,  the  mechanism  will  yield  and  the  machine  will  not  meet  undue 


FIG.  460. 

strain.  In  addition  to  its  action  as  an  automatic  relief,  the  spring  forms  also,  with  the 
connecting  rod  of  adjustable  length,  a  device  to  regulate  the  time  and  duration  of  closure 
of  the  gripping  dies  with  regard  to  the  advance  of  the  heading  dies  on  the  plunger,  as 
may  be  required  for  various  sizes  of  work." 

The  machine  described  above  is  of  the  "  grip-and-plunge  "  type. 
In  the  "  hammer-header"  form  of  heading  machine,  there  are,  for 
a  square  head,  five  hammers,  one  striking  on  the  top  and  one  on 
each  of  the  four  faces  of  the  head,  simultaneously.  In  this  ma- 
chine, the  head  is  molded  by  a  succession  of  relatively  light  blows 
while  it  is  cooling.  An  objection  urged  against  this  form  is  that 


112  MACHINE    DESIGN. 

the  -bond  between  the  head  and  shank  may  be  destroyed  by  a 
"  cold-shut  "  at  the  point  of  juncture. 

2.  NUT- BLANKS  are  made  by  several  processes.     In  the  "  hot 
pressed  "  machine,  the  nut  is  formed  in  a  die,  pierced,  and  crowned, 
and  is  then  placed  in  the  holder  of  a  "  burring  machine  "  in  which 
revolving  cutters  remove  the  rough  edges.     In  "  hot  forging  ma- 
chines," the  nut  is  forged  smooth  by  hammers  automatically  oper- 
ated ;  and,  in  "  cold  pressing,"  the  flat  bar  is  fed  between  the  rolls 
of  the  machine,  cut  into  blanks,  and  a  nut  made  complete  at  each 
revolution.     Finally,  if  desired,  the  nut  is  faced  and  chamfered  in 
a  facing  machine. 

While  the  cold-punched  nut  meets  extensive  service  in  struc- 
tural and  other  work,  the  rigid  specifications  of  the  Bureau  of 
Steam  Engineering,  U.  S.  Navy,  permit  the  use  of  hot-pressed 
nuts  only.  With  regard  to  this  question,  the  Engineer-in-chief  says  : 

"  In  making  a  cold-punched  nut,  either  of  wrought  iron  or  steel,  the  fibre  of  the  metal 
is  injured  and  its  full  strength  can  be  restored  only  by  bringing  the  nut  to  a  welding 
heat  and  finishing  it  under  the  hammer,  as  with  the  hand-made  forged  nut.  The  hot- 
pressed  nut,  on  the  contrary,  although  not  so  perfect  as  that  made  by  hand  forging,  ap 
preaches  the  latter  so  nearly  that  it  can  be  reamed,  tapped,  finished,  and  used  with 
fair  degree  of  safety." 

The  injurious  effects  upon  boiler-plate  of  punching  rivet-holes 
will  be  discussed  in  the  succeeding  chapter.  In  1878,  Mr.  David 
Townsend  *  made  some  experiments  which  show  the  flow  of  metal 
in  nuts  punched  cold  under  the  conditions  of  his  test.  He  found 
that  both  the  top  (nearest  the  punch)  and  bottom  faces  of  the  nut 
were  depressed ;  that  the  lower  diameter  was  increased,  making 
the  sides  tapering ;  and  that  a  portion  of  the  blank  punched  from 
the  hole  had  flowed  into  the  body  of  the  nut  throughout  a  zone 
nearly  half  as  deep  as  the  nut  and  beginning  almost  at  the  top 
face  of  the  latter.  The  original  depth  of  the  nut  was  1.75  in.  ; 
that  of  the  core  removed  was  1 .063  in.  The  density  of  the  latter 
was  found  to  be  the  same  as  that  of  the  metal  before  punching. 
Therefore,  a  volume  of  metal,  whose  sectional  area  was  that  of  the 
core  and  whose  length  was  1.75  —  1.063  =  0.687  ins.  was  forced 
into  the  body  of  the  nut.  It  is  apparent  that  the  stress  was 
severe. 

3.  THREADING  AND  TAPPING.  —  Bolts  are  threaded  in  the  lathe, 
or  by  hand-operated  dies,  or  in  the  bolt-cutter,  the  latter  being 

*  Jour.  Franklin  Institute,  March,  1878. 


SCREW   FASTENINGS.  113 

practically  but  a  set  of  revolving  dies  into  which  the  bolt-blank  is 
fed  at  the  required  axial  speed.  The  bolt-cutter  produces  usually 
a  full  thread  at  one  cut  with,  in  consequence,  greater  stress  in  the 
bolt  metal  and  greater  pressure  upon  the  lead-screw  than  in  the 
lathe  where  the  same  thread  would  be  made  in  several  cuts. 
Square  threads  or  those  requiring  unusual  accuracy  of  workman- 
ship require  lathe-work.  The  merits 
of  the  bolt-cutter  lie  in  the  rapidity 
and  cheapness  of  execution  and  the 
fact  that  its  product  is  sufficiently 
accurate  for  all  ordinary  purposes. 

Fig.  47  shows  a  threading  tool 
which  is  illustrated  herein  through 
the  courtesy  of  the  Rivet-Dock* 
Company,  Boston,  Mass.  The  dis- 
advantages of  the  single-point  thread 
tool  used  in  lathe  work  are :  the 
difficulties  of  keeping  the  exact 
angle  in  grinding,  of  setting  with  FIG 

the  small    thread-gauge,   the    suc- 
cession of  cuts,  necessarily  light,  to  prevent  burning  the  point,  and 
the  repeated  stops  to  test  with  a  limit-gauge  or  master-nut. 

The  thread-cutter  shown,  is  a  simple  disc  of  tool  steel  having 
ten  teeth,  each  of  the  latter  being  longer  radially  than  the  one  pre- 
ceding. In  operation,  a  cut  is  run  with  each  tooth.  There  are 
thus,  in  effect,  ten  cutting  tools,  the  leading  ones  suitably  shaped 
for  roughing  out  and  the  final  tooth  proportioned  for  finishing  with 
accuracy.  The  single-point  tool  both  roughs  and  finishes,  while 
the  final  tooth  of  the  cutter  does  finishing  work  only.  The  cutter 
is  mounted  on  a  steel  slide,  the  latter  having  a  movement  to  and 
from  the  work  by  means  of  an  eccentric  stud  in  the  hub  of  the 
lever.  The  lever,  in  moving  the  slide,  engages  the  pawl  and 
rotates  the  cutter  one  tooth  for  the  next  cut.  The  heel  of  the 
tooth  in  action  rests  upon  a  stop,  which  takes  the  strain  of  cutting. 
The  stud  extends  through  the  lever-hub  and  is  secured  on  the 
back  by  an  arm  with  pin-stop  engaging  ten  holes  so  spaced  that 
changing  the  stop  from  one  hole  to  another  moves  the  slide  and 
cutter  a  fraction  of  a  thousandth  of  an  inch  forward,  thus  giving 
the  necessary  adjustment  for  fine  fits  and  provision  for  exact  dupli- 
cation. 


MACHINE   DESIGN. 


Bolt-threads  are  produced  also  by  cold  rolling.  For  the  de- 
scription of  this  process  which  follows,  acknowledgment  is  due  to 
J.  H.  Sternbergh,  Esq.,  President  of  the  American  Iron  and  Steel 
Manufacturing  Company. 

"  The  machine  is  horizontal  and  of  simple  construction.  It  has  a  stationary  die  with 
threads  cut  on  the  face  of  the  latter  at  a  certain  angle.  Another  die,  having  threads 
cut  on  its  face  also,  is  held  in  a  reciprocating  cross-head.  The  bolt-blank  is  placed 
perpendicularly  between  the  two  dies  and  the  thread  is  produced  by  compression  in 
rolling  the  blank  between  the  latter.  The  distance  between  the  apices  of  the  dies  is  the 
same  as  the  diameter  of  the  bolt  at  the  root  of  the  thread.  For  a  bolt  of,  say,  |^-inch 
diameter,  the  dies  are  about  ten  inches  long  and  the  blank  is  rolled  throughout  nearly 
the  whole  length  of  the  die,  one  operation  producing  the  thread.  A  portion  of  the  latter 
is  actually  raised  above  the  external  circumference  of  the  bolt  and  no  metal  whatever  is 
cut  away.  Great  accuracy,  however,  is  required  as  to  the  diameter  of  the  blank  bolt  in 
order  to  produce  uniform  and  perfect  threads." 

There  are  various  types  of  machines  for  threading  nuts.  In  one 
well-known  automatic  nut-tapper,  the  blank  nuts  are  placed  in  a 
receptacle  on  the  top,  from  which  they  are  conveyed  to  the  taps 
by  means  of  guide-ways.  After  being  threaded,  the  nuts  are 
ejected  automatically.  It  is  stated  that  one  operator  can  attend 
ten  machines  and  produce  about  1 80,000  nuts  per  day. 

32.     Materials. 

The  specifications  (1901)  of  the  Bureau  of  Steam  Engineering, 
U.  S.  Navy,  for  bolts  and  nuts  of  steel  and  iron  are  as  follows  : 

RODS  FOR  BOLTS,  STUDS,  AND  RIVETS. 

I.  The  physical  and  chemical  characteristics  of  rods  for  bolts,  studs,  and  rivets  are 
to  be  in  accordance  with  the  following  table  : 


Class. 

Material. 

Minimum 
Tensile 
Strength. 

Minimum 
Elastic 
Limit. 

Minimum 
Elongation. 

Maximum 
Amount  of  — 

P. 

S. 

Lbs.fer 

Lbs.per 

Per  cent. 

sq.  in. 

sf.  in. 

in  8  Inches. 

Class  A. 

Open-hearth 

75,000 

40,000 

23 

.04 

•03 

Cold  and  quench 

nickel  or 

bend  about  an 

carbon 

inner  diameter 

steel. 

equal     to     the 

thickness  of  the 

test     piece    in 

each      case. 

Quenching 

temperature 

80°  to  90°  F. 

Class  B. 

Open-hearth 

58,000 

30,000 

28 

.04 

.03     I  Inner     diameter 

carbon 

:     equal    to     one 

steel. 

j     half  the  thick- 

1     ness. 

SCREW   FASTENINGS.  115 

If  the  contractor  desires,  and  so  states  on  his  orders,  the  Bureau  will  direct  that  the 
inspection  of  the  rods  be  made  at  the  place  of  manufacture  of  the  bolts,  studs  or  rivets 
instead  of  at  the  place  where  the  rods  are  rolled. 

2.  Kind  of  Material.  — The  steel  shall  be  made  by  the  open-hearth  process,  shall 
contain  not  more  than  four  one-hundredths  of  I  per  cent,  of  phosphorus,  nor  more  than 
three  one-hundredths  of  I  per  cent,  of  sulphur. 

3.  Surface  and  other  Defects.  —  The  rods  must  be  true  to  form,  free  from  seams, 
hard  spots,  brittleness,  injurious  sand  or  scale  marks,  and  injurious  defects  generally. 

4.  Test  Pieces.  —  If  the  total  weight  of  rods,  all  of  the  same  diameter,  and  rolled 
from  the  same  heat,  amounts  to  more  than  6  tons,  the  inspector  shall  select  at  random 
six  tensile  test  pieces,  three  cold-bending  test  pieces  and  three  quench-bending  pieces  ; 
but  if  the  weight  is  less  than  6  tons,  one  half  of  that  number  of  test-pieces  will  suffice. 
If,  however,  the  rods  in  one  heat  are  not  of  the  same  diameter,  then  the  inspector  will 
take  such  additional  test  pieces  as  he  may  consider  necessary  according  to  the  number 
of  different  sizes  of  rods  in  the  heat.     All  of  the  test  pieces  shall  be  taken  from  rods 
finished  in  the  rolls  and,  when  practicable,  but  one  piece  will  be  cut  from  each  rod 
selected  for  test.     Should  any  test  piece  be  found  too  large  in  diameter  for  the  testing 
machine,  the  piece  may  be  prepared  for  test  in   the  manner  prescribed  for  forgings. 
The  tensile  tests  for  rounds  fy  inch  in  diameter  and  less,  shall  be  made  on  the  largest 
sizes  available  and  the  elongation  measured  on  a  length  equal  to  eight  times  the  diam- 
eter. 

5.  Bending  Tests.  — The  cold  and  quench  test  pieces  of  Class  Ai  rods  shall  stand 
bending  through  an  angle  of  1 80°  around  a  curve,  the  inner  diameter  of  which  is  equal 
to  the  diameter  of  the  rod.     The  cold  and  quench  bends  of  Class  A2  rods  shall  stand 
bending  through  an  angle  of  1 80°  around  a  curve,  the  inner  diameter  of  which  is  equal 
to  one  half  the  diameter  of  the  rod.     The  quench  test  piece  shall  be  heated  to  a  dark 
cherry  red  in  daylight,  and  plunged  into  fresh  clean  water  at  a  temperature  between 
80°  and  90°  F.     No  bending  test  will  be  satisfactory  if  any  cracks  are  to  be  seen  on 
the  outside  of  the  bent  portion. 

FINISHED  BOLTS,  STUDS,  AND  RIVETS,  CLASSES  A  AND  B. 

After  the  rods  to  be  made  up  into  bolts,  studs,  and  rivets  have  been  tested  as  pre- 
viously described,  the  finished  articles  shall  be  tested  by  lots  of  500  pounds  or  fraction 
thereof,  one  piece  being  taken  to  represent  the  lot.  The  failure  of  10  per  cent,  of  the 
lots  of  500  pounds  to  stand  the  specified  tests  in  a  satisfactory  manner  will  render  the 
whole  of  any  delivery  liable  to  rejection. 

Salts  and  Studs.  — When  the  bolts  or  studs  are  of  sufficient  length  in  the  plain  part 
to  admit  of  being  bent  cold,  they  must  stand  bending  double  to  a  curve  of  which  the 
inner  radius  is  equal  to  the  radius  of  the  bolt  or  stud,  without  fracture. 

When  bolts  or  studs  are  not  of  sufficient  length  in  the  plain  part  to  admit  of  being 
bent  cold,  the  threaded  part  must  stand  bending  cold  without  fracture  as  follows  : 

If  of  l/2  inch  diameter  or  less 35° 

If  above  %  inch  diameter  and  under  I  inch 3°° 

If  I  inch  diameter  or  over .        25° 

Where  the  bending  tests  can  not  be  applied,  the  two  following  hammer  tests  must  be 
substituted  : 

(a)  The  test  piece  to  stand  flattening  out  cold  to  a  thickness  equal  to  one  half  its 
original  diameter  without  showing  cracks. 

(t>)  The  test  piece  to  stand  flattening  out,  while  heated  to  a  cherry-red  heat,  to  a 
thickness  equal  to  one  third  its  original  diameter  without  showing  cracks. 


n6 


MACHINE    DESIGN. 


Surface  Inspection.  —  ( i)  All  bolts  and  studs  shall  be  free  from  surface  defects. 

(2)  All  bolts  are  to  be  headed  hot,  and  the  heads  made  in  accordance  with  the  U. 
S.  standard  proportions  unless  otherwise  specified.     The  head  must  be  concentric  with 
the  body  of  the  bolt. 

(3)  The  threads  must  be  of  the  U.  S.  standard  unless  otherwise  specified,  and  must 
be  clean  and  sharp.     The  threads  of  Classes  A  and  B  bolts  may  be  either  chased  or  cut 
with  a  die,  but  the  threads  of  body-bound  bolts  must  be  chased  and  must  extend  far 
enough  down  so  that  when  the  nut  is  screwed  home  there  will  be  not  more  than  one 
and  one  half  threads  under  it.     The  plain  part  of  body-bound  bolts  must  be  turned  in  a 
lathe  to  fit  accurately  in  the  bolt  hole. 

STEEL  AND  IRON  NUTS. 
(  To  be  used  with  class  A  and  B  bolts  and  studs. ) 

1.  One  tensile  and   one  bending   test  bar   from  each   lot   of    1,000   pounds   of 
material  or  less  from  which  nuts  are  to  be  made  shall  be  selected  by  the  inspector  for 
test. 

2.  The  material  (whether  steel  or  iron)  shall  show  a  tensile  strength  of  at  least 
48,000  pounds  per  square  inch  and  an  elongation  of  at  least  25  per  cent,  in  8  inches. 
A  bar  y2  inch  square  or  %  inch  in   diameter  shall  bend  back  cold  through  an  angle  of 
180°  without  showing  signs  of  fracture. 

3.  The  nuts  must  be  free  from  surface  defects  and  the  threads  clean,  sharp,  and  well 
fitting. 

4.  The  dimensions  of  threads  must  be  in  conformity  with  the  United  States  standard 
unless  otherwise  specified. 

5.  The  nuts  must  be  hot-pressed  and  reamed  before  threading,  the  holes  to  be  cen- 
tral and  square  with  the  faces.     All  nuts  must  fit  on  the  bolts  without  shake. 


FORCINGS. 
i .  The  physical  and  chemical  characteristics  are  to  be  in  accordance  with  the  fol- 


lowing table  : 


Class. 

Material. 

Treatment. 

Minimum'  Minimum 
Tensile        Elastic 
Strength,  j     Limit. 

Minimum 
Elonga- 
tion. 

Maximum 
Amount  of  — 

Cold  Bend 
About  an 
Inner  Diam 
eter  of— 

P. 

S. 

Lbs.per 
*/.  in. 

Lbs.per 
sq.  in. 

Per  crnt. 
in  a  in. 

High 
Grade, 

Open-hearth 
nickel  steel. 

Annealed 
and  oil 

95,000 

65,000 

21 

.06 

.04 

One  inch 
through 

tempered. 

180°. 

Class  A. 

Open-hearth 

Annealed. 

80,000 

50,000 

25 

.06 

.04 

One  inch 

either  nickel 

Oil  tem- 

through 

or  carbon 

pered  op- 

180°. 

steel. 

tional. 

Class  B. 

Open-hearth 

Annealed. 

60,000 

30,000 

30 

.06 

.04 

Half  inch 

carbon  steel. 

through 

180°. 

6.  Nuts  to  be  used  about  machinery  must  fit  so  tight  that  it  will  be  necessary  to  use 
a  wrench  to  turn  them.     All  other  nuts  must  be  at  least  thumb  tight. 

7.  For  the  purpose  of  test  all  nuts  which  fulfill  the  preceding  requirements  will  b< 
divided  into  lots  of  500  pounds  or  less,  and  two  nuts  from  each  lot  selected  by  the  in 
specter  for  test  as  follows  : 


SCREW   FASTENINGS.  117 

(a)  One  of  the  two  shall  stand  flattening  out  cold  to  a  thickness  equal  to  one  half  its 
original  thickness  without  showing  cracks. 

(/>)  The  other  shall  stand  flattening  out  (when  heated  to  a  cherry  red  in  daylight), 
to  a  thickness  equal  to  one  third  of  its  original  thickness  without  showing  cracks. 

8.  The  failure  to  stand  these  tests  will  subject  the  lot  represented  by  them  to  rejec- 
tion. The  failure  of  10  per  cent,  of  the  lot  to  pass  the  tests  will  render  the  whole  order 
liable  to  rejection. 

For  bolts  requiring  unusual  strength,  the  metals  described  under 
"  Forgings  "  are  specified.  Thus,  connecting  rod  bolts  are  made 
from  "  High  Grade  "  forgings  as  above. 

For  wrought  iron  and  various  alloys  and  bronzes,  the  maximum 
tensile  strength  per  sq.  in.  of  cross  section  is  taken  as  : 

Wrought  Iron        50,000  Ibs. 

Alloy:  Cu88%,  Sn  10%,  Zn  2% 2o,ooo  '< 

Phosphor  Bronze,  rolled      40,000  " 

Muntz  Metal,  rolled         40,000  " 

Manganese  Bronze,  rolled 50,000  " 

Tobin  Bronze 50,000  " 

Naval  Brass  ....        50,000  " 

The  specifications  (1900),  of  a  prominent  railroad  company  fix 
requirements  for  stay-bolt  iron,  as  follows  : 

"  The  material  desired  is  fagoted  iron,  free  from  admixture  of  steel  and  preferably  box 
piled,  the  rilling  of  the  box  being  small  rods.  It  shall  show  when  nicked  on  either 
side  and  then  broken,  a  fracture  with  long  fiber  with  sound  welds.  The  iron  must  be 
smoothly  rolled,  free  from  slivers  and  depressions,  and  shall  be  truly  round  within  .01 
of  one  inch.  It  shall  not  be  more  than  .005  of  one  inch  above  and  not  more  than  .010 
of  an  inch  below  nominal  size.  This  to  insure  freedom  from  jamming  in  the  thread- 
ing dies. 

"  Sample  bars  will  be  required  to  meet  the  following  physical  test:  They  shall  show 
when  tested  in  full  size  as  rolled,  a  tensile  strength  of  not  less  than  48,000  pounds  per 
square  inch,  with  an  elongation  of  not  less  than  25  per  cent,  in  8  inches.  One  piece  from 
each  of  the  two  sample  bars  shall  be  subjected  to  tensile  test  and  one  piece  from  each  of 
them  shall  be  threaded  in  dies  with  a  sharp  "V"  thread  12  to  one  inch  and  firmly 
screwed  through  two  holders,  having  a  clear  space  between  them  of  5  inches.  One  of 
the  holders  shall  be  of  such  form  and  length  that  the  bolt  shall  be  rigidly  held,  so  as  to 
prevent  rocking.  This  holder  will  be  rigidly  secured  to  the  bed  of  a  suitable  machine 
and  the  holder  at  the  other  end  will  be  vibrated  in  a  direction  at  right  angles  to  the 
axis  over  a  space  of  }£  of  an  inch,  so  that  the  end  of  the  specimen  shall  be  deflected 
alternately  ^  of  an  inch  on  each  side  of  the  center  line.  When  thus  tested  acceptable 
iron  should  show  not  less  than  2,200  double  vibrations  before  breakage. 

"  If  the  test  of  either  of  the  bars  shows  a  tensile  strength  of  less  than  48,000  pounds 
per  square  inch  in  an  original  section  or  an  elongation  less  than  25  per  cent,  in  a  sec- 
tion originally  8  inches  long,  or  if  either  bar  stands  less  than  1,700  double  vibrations,  or 
if  the  two  give  an  average  of  less  than  1,900  double  vibrations  before  breakage,  the  pile 
represented  by  such  two  bars  will  be  rejected  and  returned  to  the  maker.  In  addition, 
those  bars  which  fail  to  meet  the  requirements  as  to  rolling  will  also  be  rejected  and 
returned." 


MACHINE   DESIGN. 


33.     Nut-Locks. 

As  has  been  shown  previously,  the  pitch-angle  of  screw-fasten- 
ings is  so  small  that  the  screw  cannot  possibly  "overhaul,"  i.  e., 
no  static  axial  load,  however  great,  will  cause  the  nut  to  back  off. 
On  the  other  hand,  on  such  a  screw,  when  exposed  to  shock  or  to 
repeated,  even  though  small,  vibrations,  the  nut  will  loosen  inevitably. 
Dr.  Weisbach  *  has  discussed  fully  and  clearly  the  effect  upon  the 
nut  of  these  external  forces.  When  the  joint  is  subjected  to  shock 
or  vibration,  work  is  done  upon  all  of  its  parts.  The  work  trans- 
ferred to  the  nut,  expends  itself  in  producing  elastic  oscillations  in 
the  material  of  the  latter,  with  corresponding  stresses  of  tension 
or  compression,  and,  therefore,  at  any  instant,  a  resultant  stress. 
When  the  moment  of  this  resultant  is  equal  to  the  moment  of  nut- 
friction,  any  further  shock  or  vibration  will  cause  the  nut  to  yield. 
It  is  evident,  therefore,  that  the  force  with  which  the  nut  is  screwed 
home,  fixes  the  magnitude  of  the  shock  which  will  loosen  it. 
Hence,  nuts  which  can  be  set  up  with  but  moderate  pressure,  as 
on  shaft  bearings,  especially  need  locking  arrangements.  Again, 
the  effect  of  small  vibrations,  if  they  follow  each  other  with  sufficient 

frequency,  seems  to  be  cumu- 
lative, so  that,  even  when  nuts 
are  set  up  with  the  greatest  per- 
missible force  on  solid  supports, 
as  the  fish-plates  of  rails,  they 
will,  if  unlocked,  back  off  under 
these  conditions.  The  usual  de- 
vices for  locking  a  fastening  nut 
are  the  check-nut,  set-screws, 
spring-washers,  and  lock-plates. 
The  nut  itself  is  sometimes 
made  elastic  or  the  thread  self- 
locking. 

i.  CHECK-NUTS. — A  check- 
nut  is  essentially  a  friction -brake 
for  the  fastening  nut.  Assume, 
as  in  Fig.  48,  a  bolt,  A,  with 
fastening  and  check  nuts,  B  and  C,  respectively.  Let  the  lower 
nut  be  held  and  the  upper  be  screwed  against  it  as  tightly  as 

*"  Mechanics  of  Engineering,"  Vol.  III.,  Parti.,  Sec.  II.,  1896,  p.  605. 


FIG.  48. 


SCREW   FASTENINGS.  1 19 

the  strength  of  the  bolt  permits.  There  will  be  developed  a 
pressure,  P,  between  the  adjoining  nut-faces,  and  the  nuts  B  and 
C  will  transmit  this  pressure  to  the  lower  and  upper  surfaces,  re- 
spectively, of  the  bolt  threads.  Hence,  a  unit  tensile  stress,/, 
will  exist  within  the  bolt  section,  D-E,  included  between  the  limits 
of  action  of  the  nuts  upon  the  bolt.  This  stress  will  not  be  present 
elsewhere.  If  now  the  bolt  be  subjected  to  shock,  the  fastening 
nut,  B,  cannot  back  off  unless  either  its  own  thread-friction  and 
that  of  the  lower  nut  be  overcome  and  the  two  withdraw  together, 
or  the  nut,  B,  have  a  sufficient  impulse  to  move  independently,  de- 
spite the  friction  between  the  nut-faces.  In  either  case,  the  check- 
nut  acts  as  a  brake  upon  the  fastening  nut. 

Again,  assume,  as  in  the  left-hand  half  of  the  figure,  that  the 
bolt  is  used  for  securing  the  cap,  F,  of  a  shaft-bearing.  Let  the 
lower  nut,  C,  be  first  screwed  down  until  the  required  pressure,  Pv 
is  produced  upon  the  cap  and  then  the  upper  nut,  B,  be  screwed 
home  as  before,  developing  the  pressure,  P,  between  the  nut-faces. 
The  nut,  C,  is  now  subjected  to  a  downward  force,  P,  and  an  up- 
ward force,  Pv  with  a  resultant,  P  —  Pv  acting  on  the  bolt-threads. 
There  are  three  possible  cases  : 

(a)  If  Pl  >  P,  the  resultant  force  is  upward,  the  lower  nut  bears 
on  the  lower  surfaces  of  the  bolt-threads  and  aids  in  sustaining  the 
axial  load,  Pv  upon  the  bolt. 

(b)  If  Pl  =  P,  the  resultant  force  is  zero.     Hence  the  lower  nut 
is  unloaded  and  has  no  pressure  on  either  the  upper  or  lower  sur- 
faces of  the  bolt  threads. 

(c)  If  Pl  <  P,  the  resultant  force  is  downward,  the  lower  nut 
bears  on  the  upper  surfaces  of  the  bolt-threads,  does  not  aid  in 
sustaining  the  axial  load,  and  produces  an  additional  tensile  stress, 
as  at  D-E. 

In  both  (a)  and  (c),  thread-friction  exists  with  the  lower  nut  and 
the  latter  acts  as  a  brake  ;  in  (a)  only  this  nut  aids  in  sustaining 
the  axial  load,  Pv  upon  the  bolt,  which  load  in  (&)  and  (c)  is  borne 
wholly  by  the  upper  nut.  The  fastening  and  check-nuts  are 
frequently  of  different  thicknesses.  The  discussion  as  above  — 
adapted  largely  from  Weisbach  —  shows  that  the  upper  nut  may 
bear  the  entire  load  and  should  be  the  thicker  of  the  two,  although, 
in  the  absence  of  a  thin  wrench,  the  reverse  is  often  the  case.  In 
practice,  the  lower  nut  is  screwed  down  and  home  and  the  upper 
nut  almost  entirely  so.  Then,  the  latter  is  held  with  the  wrench 


120 


MACHINE   DESIGN. 


and  the  nut,  C,  is  forced  backward  through  a  slight  angle  until  it 
binds  on  the  upper  nut. 


FIG.  49. 


FIG.  50. 


FIG.  51. 


2.  SET-SCREWS.  —  The  set-screw,  bearing  upon  a  cylindrical 
prolongation  of  the  nut,  is  the  most  effective  locking  device  for 
heavy  nuts  requiring  to  be  frequently  removed  as,  for  example, 
those  on  the  connecting  rods  and  main  bearing  caps  of  marine 
engines.  Fig.  35  shows  a  bolt  for  the  former  which  is  fitted  with 
a  "collar-nut"  and  two  set-screws  —  one  for  locking  the  nut,  the 
other  for  holding  the  bolt  when  backing  off  the  nut.  Table 
XXXVI.  gives  the  proportions  of  such  collar  nuts  and  of  the 
dowelled  stop-ring  into  which  the  set-screw  is  tapped.  Fig.  49 
shows  a  similar  nut,  omitting  the  stop-ring  and  groove,  the  pro- 
portions for  typical  sizes  of  which,  in  inches,  are  : 


Diameter 

Least  Value  of  H  for 

of 
Bolt. 

A 

B 

C 

D 

E 

F 

G 

Wrought  Iron  or 
Brass. 

Cast  Iron. 

1 

2 

4 

f 

4 

1 

I 

If 

1 

i 

I 

Ij 

I 

ft 

! 

i 

I  \ 

6 

9 

6 

2 

If 

I* 

I          Ij- 

if 

if 

3.  ELASTIC  NUTS.  —  Fig.  50  shows  the  nut  made  by  the  Na- 
tional Elastic  Nut  Company.  The  blank  is  cut  from  a  flat  steel 
bar,  bent  into  a  ring  with  a  lap  on  the  side,  pressed  in  a  die  into 
the  shape  of  a  finished  nut,  and  finally  tapped  with  special  minus 
taps,  -jj-g-  under  size.  When  screwed  on  the  bolt,  the  split  side  is 
forced  open  about  -^-^  of  an  inch,  giving  the  nut  a  constant  grip. 

The  Wiles  lock-nut,  shown  in  Fig.  51,  has  a  slot  milled  half 
way  through  of  a  width  equal  to  the  pitch.  When  the  nut  is  in 
place,  the  walls  of  the  slot  are  brought  slightly  together  by  a  set- 
screw,  thus  gripping  the  bolt-thread. 


SCREW   FASTENINGS. 


121 


TABLE  XXXVI. 

COLLAR-NUTS  WITH  LOCKING  SCREWS. 
(UNION  IRON  WORKS.) 


Nut 


Set-Screw. 


Dowel. 


4.  SELF-LOCKING  THREADS.  —  In  the  "  Harvey  Grip  "  thread, 
the  bolt  has  a  ratchet-thread,  under  cut  on  the  bearing  side  at 
about  5  degrees  less  than  a  right  angle  to  the  axis  of  the  bolt  and 
the  apex  of  the  thread  is  cut  to  a  knife-edge.  The  nut  also  has  a 
ratchet-thread,  the  bearing  side  of  which  is  about  5  degrees  greater 
than  a  right  angle  to  the  axis  of  the  nut.  There  is  thus  a  cavity 


122  MACHINE   DESIGN. 

of  about  10  degrees  between  the  bolt  and  nut-threads ;  and,  when 
the  nut  is  screwed  home,  the  axial  pressure  upon  it  forces  the  thin 
bolt-threads  out  into  the  nut-threads,  thus  filling  the  cavity  and 
locking  the  nut. 

In  another  locking  device  of  this  class,  the  thread  is  triangular 
with  the  V  cut  off  at  %  of  its  height  from  the  top  and  filled  in  at 
*<i  the  height  from  the  bottom.  The  thread  is  thus  about  yz  the 
height  of  the  sharp  V  type  and  has  broad  flats.  The  threaded 
portion  of  the  bolt  has  a  taper  of  I  in  48  to  the  axis,  while  the 
nut  has  the  usual  thread  and  is  tapped  straight.  Hence,  as  the 
latter  moves  up  the  conical  surface  of  the  bolt,  the  metal  of  the 
broad-topped  bolt-threads  flows  into  the  narrower  nut-spaces  caus- 
ing the  threads  to  lock  tightly.  The  fibre  of  the  metal  displaced  in 
screwing  the  nut  on,  is  broken  when  the  nut  is  unscrewed. 

5.  SPRING- WASHERS. — A  spring-washer,  such  as  is  shown  in 
Fig.  52^,  is  used  frequently  as  a  locking  device.  It  is,  in  effect, 
one  convolution  of  a  helical  spring  which  is  interposed  between 
the  nut  and  the  member  to  be  secured.  The  nut  is  screwed  home 
upon  the  washer  and  the  elasticity  of  the  latter  produces  a  pres- 
sure upon  the  nut  and,  therefore,  increased  frictional  resistance  of 
the  threads. 


Fig.  *)2.b  represents  one  form  of  the  Verona  nut-lock,  a  spring 
washer  which  is  not  curved  helically  as  a  whole,  but  has  the 
points  thrown  out,  thus  giving  added  power  and  cutting  edges 
which  engage  the  abutting  surfaces.  The  tail-piece  extension  is 
used  in  railway  construction  in  keeping  the  lock  clear  of  the  oval 
holes  punched  in  fish-plates. 

The  National  Lock  Washer,  shown  in  Fig.  52^,  has  a  sharp  rib 
on  its  inner  circumference  and  next  the  nut-face.  When  the  nut 
is  set  up,  it  meets  the  rib,  which,  being  harder  than  the  nut,  pro- 
gressively upsets  and  forces  some  of  the  metal  of  the  latter  into 
the  bolt-threads.  Hence,  the  nut  is  held  not  only  by  spring  pres- 
sure but  by  a  partially  locked  nut-thread. 


SCREW   FASTENINGS. 


I23 


Fig.  53  illustrates  the  Excelsior  Double  Nut  Lock  as  applied  to 
a  fish-plate.  It  is  of  serpentine  form  with  two  loops  and  out- 
thrown  points,  and  is  bent  into  a  shallow  elliptic  curve.  Since  it 
embraces  two  bolts,  it  cannot  rotate  with  the  nuts. 


FIG.  53. 

6.  LOCK-PLATES.  —  The  nut  may  be  kept  from  reversing  by  a 
lock-plate  fastened  at  one  side  of  it,  as  in  Fig.  54.  The  plate  is 
held  by  a  cap-screw  tapped  into  the  flange  to  be  secured  and  is 
essentially  but  a  thin  wrench  engaging  the  nut.  The  form  shown 
will  hold  the  nut  in  either  of  two  positions,  i.  e.,  with  a  side  of  the 
nut  parallel  or  perpendicular  to  the  centre-line,  B-C.  Lock -plates, 
single  or  double,  are  used  frequently  for  the  nuts  of  studs  which 
join  propeller-blades  to  the  hub.  The  plate  shown  in  Fig.  54  may 
have  a  slot  for  the  screw,  C,  concentric  with  the  bolt-centre.  In 
that  case,  the  plate  may  be  shifted  and  the  nut  locked  in  any  position. 


\A 


FIG.  54. 


FIG.  55. 


The  Jones  Tie-Bar  Lock  is  shown  in  Fig. '5 5.  It  is  a  square 
washer  with  one  end,  A,  flanged  upward  against  the  bar  and  the 
other  extremity,  B,  bent  downward  against  the  side  of  the  nut. 
The  latter  flange,  B,  is  turned  after  the  nut  is  in  place. 

7.  SPLIT  PINS.  —  Nuts  not  requiring  frequent  removal,  as  those 
of  piston  follower-bolts,  are  sometimes  fitted  with  split  pins. 
After  the  nut  is  in  place,  a  hole  is  drilled  through  the  bolt  so  that 
the  pin  when  inserted  will  bear  upon,  and  prevent  axial  move- 
ment of,  the  nut.  Such  a  lock  serves  for  but  one  position  of  the 
parts. 


124 


MACHINE   DESIGN. 


34.     Wrenches. 

i.  U.  S.  STANDARD.  — Table  XXXVII.  and  Fig.  56  — which 
are  reproduced  herein  through  the  courtesy  of  Messrs.  J.  H.  Wil- 
liams and  Company,  Brooklyn,  N.  Y.  —  give  the  proportions  of 
Engineers'  Wrenches,  Single  Head,  drop-forged,  for  the  nuts  of 
bolts  ranging  in  diameter  from  ^  inch  to  3^  inches. 


FIG.  56. 

TABLE  XXXVII. 

ENGINEERS'  WRENCHES,  SINGLE  HEAD. 
(MESSRS.  J.  H.  WILLIAMS  &  Co.) 


Number. 

For  U.S.  Standard 
Nut;  Size  Bolt. 

Opening  Finished. 

Extreme 

..ength. 

Thickness  Head. 

OO 
0 

A 

ft 

2i 
2 

f 

l\ 

I 

j 

£ 

3! 

I 

2 

_5 

4t 

3 

4 

A 

li 

¥ 

5 

A 

7^ 

\A 

6 

T97 

H 

8 

xV 

7 

£ 

I-jJjr 

9 

li 

8 
9 

!' 

ijt 

III 

13 

' 

ft 

10 

I    £ 

14^ 

f 

ii 

^ 

l}| 

16 

If 

12 

i 

2 

18. 

~  T 

X3 

| 

»& 

20; 

' 

ff 

14 

| 

2| 

22^ 

' 

rV 

15 

| 

2T9^ 

24 

16 

f 

2  f 

2* 

• 

if 

2 

$ 

2* 
29} 

• 
' 

18 

2  i 

3  1 

33 

H 

19 

2  J 

sl 

37 

|^ 

19* 

2  I 

4} 

37 

i 

20 

3 

A   4 

44 

X 

20* 

3* 

5  1 

44 

1 

SCREW   FASTENINGS. 


I25 


The  length  and  thickness  of  similar  wrenches  —  excepting  that 
the  handle  tapers  in  the  opposite  direction  —  are  given  as,  respec- 
tively, 59  inches  and  2\  inches.  It  will  be  observed  that .  the 
opening  of  these  wrenches  is  at  an  angle  of  1 5  degrees  with  the 
handle.  This  inclination  permits  the  turning  of  a  hexagon  nut 
completely  around  in  positions  where  the  swing  of  the  handle  is 
limited  to  30  degrees  —  an  important  improvement  which  origi- 
nated with  this  firm.  The  proportions  given  in  Fig.  56  are  those 
of  a  wrench  of  medium  size,  the  unit  being  the  bolt-diameter. 
These  proportions  are  modified  somewhat  as  the  wrenches  become 
very  large  or  very  small,  although  the  general  design  remains  the 
same.  Check-nut  wrenches  are  shorter  and,  of  course,  thinner. 
Their  dimensions  are  given  in  Table  XXXVIII. 

TABLE  XXXVIII. 

CHECK-NUT  WRENCHES. 
(MESSRS.  J.  H.  WILLIAMS  &  Co.) 


Number. 

For  U.  S.  Standard 
Nut  ;    Size  Bolt. 

Opening,  Finished. 

Extreme  Length. 

Thickness  Head. 

602 

.       A 

19 

4i 

H 

603 

1 

\\ 

5& 

-h 

604 

If 

A 

o 

605 

\ 

£ 

4 

i 

607 

| 

iJj 

8| 

A 

608 

| 

I  £ 

10 

I 

609 

610 

I 

:t 

11} 
I3i 

f 

2.  INTERNATIONAL  STANDARD  THREAD  (S.  I.).  —  The  origin 
and  proportions  of  this  system  of  screw-threads  have  been  de- 
scribed in  §  20.  A  special  committee  of  delegates  from  the  As- 
sociation of  German  Engineers,  the  Society  for  the  Encourage- 
ment of  National  Industry  at  Paris,  and  the  Swiss  Union  of 
Mechanical  Manufacturers  met  at  Zurich,  October  20,  1900,  to 
formulate  an  auxiliary  standard  system  of  wrench  openings  for 
nuts  and  bolt-heads.  A  conference  of  delegates  from  these  socie- 
ties, on  October  30,  1900,  adopted  and  recommended  for  interna- 
tional use  the  system  whose  rules  *  follow  : 

The  standard  openings  are  considered  as  limiting  dimensions  which  the  nut  is  not  to 
exceed  nor  the  wrench  fall  short  of. 

To  each  diameter  of  the  standard  series  corresponds  a  particular  wrench  opening. 


*  American  Machinist,  April  4,  1901. 


126 


MACHINE    DESIGN. 


The  same  openings  should  be  employed  for  diameters  specially  intercalated,  between 
the  standard  ones.  (This  evidently  means  that  where  a  bolt  of  special  diameter  is 
made,  it  should  be  given  a  head  and  nut  of  a  standard  size. ) 

The  opening  of  the  wrench  is  the  same  for  the  nut  and  for  the  head  of  the  bolt  and 
the  screw  of  the  same  diameter. 

The  same  opening  is  applicable  to  rough  nuts  and  machined  nuts. 

It  is  recommended  that  the  height  of  the  nut  be  equal  to  the  diameter,  and  of  the 
head  to  seven  tenths  of  the  diameter. 

The  following  table  gives  these  openings  for  all  the  standard  diameters  : 


Diameter  of              pitcij 
the  Screw. 

Opening  of 
the  Wrench. 

Diameter   of 
the  Screw. 

Pitch. 

Opening  of 

the  Wrench. 

mm.                     mm. 

mm. 

mm. 

mm. 

mm. 

6 

I 

12 

33 

3-5 

50 

7 

I 

13 

36 

4 

54 

8 

1-25 

15 

39 

4 

58 

9 

1-25 

16 

42 

4-5 

63 

10 

1-5 

18 

45 

4-5 

67 

ii 

1-5 

19 

48 

5 

7i 

12 

1-75 

21 

52 

5 

77 

\i 

2 
2 

11 

t 

5-5 
5-5 

82 
88 

18 

2-5 

29 

64 

6 

94 

20 

2-5 

32 

68 

6 

100 

22 

2-5 

72 

6-5 

105 

24 

3 

38 

76 

6-5 

no 

27 

3 

42 

80 

7 

116 

30 

3-5 

46 

The  wrench  openings  in  the  above  table  approximate  those  deduced  from  the  formula 
.4  diameter  (in  millimeters)  -\-  4  mm. 


CHAPTER   III. 

RIVETED  JOINTS.     THEORY   AND   FORMULA. 

35.     Rivets. 

RIVETS  are  permanent  fastenings  used  in  joining  the  parts  of 
metallic  structures,  such  as  the  framing  of  buildings  and  bridges, 
the  hulls  of  ships,  the  shells  of  steam  boilers,  and  the  plating  of 
tanks,  gasometers,  etc.  They  are  made  in  a  forging  machine 
(§  3 1),  the  dies  of  which  form  under  pressure,  from  the  heated  bar, 
a  rivet-blank  composed  of  the  head  and  the  shank  or  body.  When 
the  blank  is  reheated  and  set  in  the  joint,  a  second  head  or  point  is 
made  by  hand  or  power  from  the  metal  of  the  protruding  extrem- 
ity of  the  shank. 

36.     Proportions  of  Rivets. 

i.  HEAD  AND  POINT.  —  The  shape  of  the  head  is  usually  spher- 
ical or  that  of  a  frustum  of  a  cone ;  that  of  the  point  may  be 
spherical,  conoidal,  or  conical,  the  latter  being  the  usual  form  with 
hand-work.  Either  the  head  or  point  or  both  may  be  counter- 
sunk and  recessed  in  the  plate,  having  then  the  form  of  an  inverted, 
conical  frustum. 

In  the  United  States,  riveted  joints  are  designed  without  regard 
to  the  resistance  to  yielding  opposed  by  the  friction  between  the 
plates,  the  rivet  being  assumed  to  have  practically  the  same  func- 
tion as  that  of  a  bolt  subjected  only  to  cross-shear.  In  effect, 
however,  the  rivet  has  an  initial  tension  due  to  its  contraction  in 
cooling  ;  and,  further,  from  the  same  cause,  the  shank  is  smaller 
than  the  hole  through  which  it  passes.  Therefore,  when  the  joint 
is  loaded,  bending  stress  precedes  shearing  in  the  rivet,  and,  in 
service,  the  latter  thus  meets  compound  stress  of  which  tension  is 
a  factor. 

While,  therefore,  the  rivet  is  not  intended  for,  and  is  untrust- 
worthy in,  tension,  that  stress  acts  in  service  within  the  shank, 
producing  a  consequent  compression  and  tendency  to  shear 
within  the  head  and  point  and  to  rupture  at  the  junctions  of 
these  features  with  the  shank,  especially  if  slight  fillets  are  not 
made  at  these  places.  In  experiments  made  by  Stoney  on  the 

127 


128 


MACHINE    DESIGN. 


strength  of  iron  rivets  in  tension,  he  found  that,  with  |-inch  rivets 
with  pan  heads  and  hand-made  snap-points,  in  punched  holes,  the 
heads  or  points  flew  off  under  an  average  tensile  stress  of  12.32  tons 
per  sq.  in.  of  rivet  cross-section.  It  is  apparent  that  the  contour 
and  strength  of  these  features  of  the  rivet  are  important,  not  only 
because  of  the  stresses  met,  but,  as  in  marine  work,  bridges,  etc., 
where  minimum  weight  is  desirable. 

Good  practice,  with  regard  to  the  proportions  of  rivet-blanks 
for  general  service,  is  given  by  Table  XXXIX.  and  Fig.  57,  which 


FIG.  57. 

illustrate  cone  or  "pan-head,"  spherical  or  "button-head,"  and 
countersunk -head  types,  as  designed  by  J.  H.  Stern bergh,  Esq., 
President  of  the  American  Iron  and  Steel  Manufacturing  Com- 
pany. 

TABLE  XXXIX. 

PROPORTIONS  OF  RIVET-HEADS. 
.(AMERICAN  IRON  AND  STEEL  MANUFACTURING  COMPANY.) 


Shank, 
Diameter. 

Head. 

Form. 

Diameter, 
Least. 

Diameter, 
Greatest. 

Height. 

Angle. 

D 
G 
K 

Cone. 
Button. 
Countersunk. 

B  =  D 

c 

F 

II 

=  1-75  D 
=  1-75  G 

A  =  .875  D 
E  =  0.75  G 

35° 

K 
H 

1 

ft 

i 

ftll 

ftlJt 

4J 

.LULU 

if      ill 

It 

2 

Similar  proportions  of  Victor  Steel  Rivets,  as  made  by  the 
Champion  Rivet  Company,  are  shown  in  Table  XL.  and 
Fig.  58. 


RIVETED   JOINTS. 
—    2D 


I29 


*__ 


FIG.  58. 

The  button-head  form,  Fig.  59^,  is  widely  used  for  points  and, 
in  structural  work  especially,  for  heads  as  well,  excepting  where, 
from  lack  of  space,  the  countersunk  type,  Fig.  $c)b,  is  required. 

TABLE  XL. 

PROPORTIONS  OF  RIVET- HEADS. 
(CHAMPION  RIVET  COMPANY.) 


Diameter. 

Form. 

Diam.  Least. 

Diam.  Greatest. 

Height. 

Angle. 

D 

D 
D 
D 

Cone. 
Button. 
Steeple. 
Countersunk. 

tt» 

2     D 

\D 

D 

40° 

The  former  is  much  more  trustworthy  than  the  conical  or  steeple 
point,  Fig.  59<:,  usual  with  hand-work. 


YP 

d 


FIG.  59. 


The  pan-head,  Fig.  59,  c,  d,  is  much  employed  in  boiler  and  ma- 
rine work  generally.  The  form  is  one  of  great  strength.  The 
objections  to  it  are  its  weight  and  the  fact  that  unless  its  shortest 
diameter  is  equal  to  that  of  the  rivet-shank,  it  is  difficult  to  make 
the  latter  and  the  head  concentric. 


130  MACHINE    DESIGN. 

The  countersunk  head  or  point,  Fig.  59^,  adds  no  weight  to  the 
joint  and,  when  properly  closed,  its  wedge-like  form  gives  rigidity 
and  produces  maximum  plate -friction.  There  is,  however,  a  de- 
crease in  the  strength  of  the  plate,  owing  to  the  additional  metal 
removed  and  an  increase  in  cost  from  the  countersinking  required. 
It  is  essential  that  countersunk  heads  shall  fit  the  holes  exactly 
when  the  rivet  is  driven  home.  The  angle  of  countersink  varies 
from  15  to  45  degrees. 

2.  SHANK.  —  The  shank  is  cylindrical  throughout  the  greater 
part  of  its  length  but  tapers  slightly  toward  the  end.     Its  length 
is  equal  to  the  grip  (i.  e.,  the  combined  thicknesses  of  the  plates 
through  which  it  passes)  plus"  that  of  the  additional  metal  required 
to  fill  the  rivet-hole  and  to  form  the  point.     To  permit  the  inser- 
tion of  the  heated  and  expanded  rivet-blank,  the  rivet  holes  are 
usually   jJg  in.   larger  in   diameter   than    the   blank    when    cold. 
Again,  in  machine-riveting,  the  pressure  upon  the  hot  and  plastic 
metal  of  the  rivet  is  more  continuous  and  severe  than  in  hand- 
work, thus  forcing  more  metal  into  the  hole. 

Hence,  the  required  length  of  shank,  additional  to  the  grip,  de- 
pends upon  the  form  of  the  head,  the  length  and  clearance  of  the 
rivet-hole,  and  the  character  of  the  riveting  process.  In  aver- 
age proportions,  the  total  length  of  the  shank  is  equal  to  the  grip 
plus  1.5  times  the  diameter,  with  an  increase,  fixed  by  experiment, 
for  machine-riveting.  The  length  of  shank  required  to  make  a 
countersunk  point  is  about  that  of  the  shank-diameter. 

The  slight  tapering  of  the  shank  under  the  head,  Fig.  59^,  adds 
strength  at  their  junction  and  gives  a  better  form  for  the  conical 
hole  made  in  punching.  In  drilled  holes  a  short  countersink  is 
advantageous  at  this  point  in  removing  sharp  edges  left  by  the 
tool. 

3.  RIVET-HEADS  AND  PLATE- FRICTION. — The  results  of  Pro- 
fessor  Bach's  extensive  experiments  upon  pi  ate -friction  will   be 
given  in  §  46.     With  regard  to  the  magnitude  of  the  friction  be- 
tween the  plates  produced  by  the  pressure  of  different  forms  of 
rivet-heads,  Stoney  *  gives  the  following  results  from  tests  made 
with  steel  rivets  and  steel  plates,  the  joint  being  composed  of  a 
middle  plate  between  two  others,  all  united  by  three  rivets  in  one 
row,  the   rivets  being   thus  in   double  shear.     The  i-inch  rivets 


'Strength  and  Proportions  of  Riveted  Joints,"  1885,  p.  75. 


RIVETED   JOINTS.  131 

were  used  in  ^-inch  plates  and  the  ^-inch  rivets  in  i^-inch  plates. 
With  hand- riveting,  the  mean  frictional  resistances,  per  rivet  in 
tons,  were  : 

I-IN.  RIVET.  ^-JN.  RIVET. 

Snap  head  and  point 6.40  4.72 

Pan  head,  boiler  point.  7.36  4.52 

Pan  head,  countersunk  point 8.55  6.25 

Countersunk  head  and  point 9- 04  4-95 

As  a  whole,  these  tests  show  the  greatest  friction  for  counter- 
sunk rivets,  whose  wedge-shaped  heads,  when  properly  driven, 
produce  great  pressure  as  the  rivet  contracts.  In  other  experi- 
ments with  snap-heads  and  points,  but  with  machine-  riveting,  the 
mean  friction  per  rivet  was  9.6  tons  for  i-inch  rivets  and  5.9  tons 
for  j^-inch  rivets. 

37.     Rivet  and  Plate  Metals. 

i .  STEEL  has  very  largely  superseded  wrought  iron  for  rivets, 
plating,  shapes,  etc.,  in  all  structural,  ship,  and  boiler-work.  The 
following  extracts,  with  regard  to  chemical  and  physical  properties, 
are  taken  from  "  The  American  Standard  Specifications  for  Steel,"* 
adopted  August,  1901,  by  the  American  Section  of  the  Interna- 
tional Association  for  Testing  Materials  : 

STRUCTURAL  STEEL  FOR  BUILDINGS. 

1.  Steel  may  be  made  by  either  the  open-hearth  or  Bessemer  process. 

2.  Each  of  the  two  classes  of  structural  steel  for  buildings  shall  not  contain  more 
than  o.  10  per  cent,  of  phosphorus. 

3.  There  shall  be  two  classes  of  structural  steel  for  buildings,  namely  :  RIVET  STEEL 
and  MEDIUM  STEEL,  which  shall  conform  to  the  following  physical  qualities  : 


Tensile  strength,  Ibs.  per  sq 
Yield  point,  in  Ibs.  per  sq.  i 
Elongation,  per  cent,  in  eight 

inch, 
n.  ,  shall  not  be  less  than 
ins.,  shall  not  be  less  than 

50,000-60,000 
JT   S. 
26 

60,000-70,000 
JT.S. 

22 

STRUCTURAL  STEEL  FOR  BRIDGES  AND  SHIPS. 

1.  Steel  shall  be  made  by  the  open-hearth  process. 

2.  Each  of  the  three  classes  of  structural  steel  for  bridges  and  ships  shall  conform  to 
the  following  limits  in  chemical  composition  : 


Steel  Made  by     |     Steel  Made  by 

the  Acid  Process,     the  Basic  Process. 

Per  cent.  Per  cent. 


Phosphorus  shall  not  exceed 
Sulphur  shall  not  exceed 


0.08  0.06 

0.06  0.06 


American  Standard  Specifications  for  Steel,"  A.  L.  Colby,  1902. 


132 


MACHINE   DESIGN. 


3.  There  shall  be  three  classes  of  structural  steel  for  bridges  and  ships  namely : 
RIVET  SEEEL,  SOFT  STEEL,  and  MEDIUM  STEEL,  which  shall  conform  to  the  following 
physical  qualities  : 


Rivet  Steel. 

Soft  Steel. 

Medium  Steel. 

Tensile  strength,  Ibs.  per  sq.  in. 
Yield  point,  in  Ibs.  per  sq.  in.,  shall 
not  be  less  than 
Elongation,  per  cent,  in  eight  inches, 
shall  not  be  less  than 

50,000-60,000 

JT.& 

26 

52,000-62,000 
£T.S. 
25 

60,000-70,000 

JT.& 

23 

OPEN-HEARTH  BOILER  PLATE  AND  RIVET  STEEL. 

1.  Steel  shall  be  made  by  the  open-hearth  process. 

2.  There  shall  be  three  classes  of  open-hearth  boiler-plate  and  rivet-steel,  namely  : 
FLANGE  OR  BOILER  STEEL,  FIRE-BOX  STEEL,  and  EXTRA  SOFT  STEEL,  which  shall 
conform  to  the  following  limits  in  chemical  composition  : 


Flange  or  Boiler  Steel. 
Per  cent. 

Fire-  Box  Steel. 
Per  cent. 

Extra  Soft  Steel. 
Per  cent. 

Phosphorus  shall  not  ex- 
ceed 
Sulphur  shall  not  exceed 
Manganese. 

(  Acid,      0.06 
\  Basic,     0.04 
0.05 
0.30  to  0.60 

{  Acid,      0.04 
\  Basic,     0.03 
0.04 
0.30  to  0.50 

0.04 
0.04 
0.30  to  0.50 

4.  The  three  classes  of  open-hearth  boiler-plate  and  rivet-steel,  namely :  FLANGE 
OR  BOILER  STEEL,  FIRE-BOX  STEEL,  and  EXTRA  SOFT  STEEL,  shall  conform  to  the 
following  physical  qualities  : 


Flange  or  Boiler 
Steel. 

Fire-Box  Steel. 

Extra  Soft  Steel. 

Tensile  strength,  Ibs.  per  sq.  in. 
Yield  point,  in  Ibs.,  per  sq.  in.,  shall 
not  be  less  than 
Elongation,  per  cent,  in  eight  inches, 
shall  not  be  less  than 

55,000-65,000 

JT.S. 

25 

52,000-62,000 

JT.S. 

26 

45,000-55,000 
JT.  S. 

28 

In  all  of  the  steels  described  above,  modifications  are  made,  for 
thin  and  thick  material,  in  the  required  elongation. 

In  general,  steel  rivets  should  be  made  by  the  open-hearth  pro- 
cess, be  low  in  sulphur  and  phosphorus,  and  be  of  a  soft,  ductile 
character.  The  following  table  gives  the  average  of  a  number  of 
analyses  of  Victor  Steel  Rivets  : 


Phosphorus,  per 
Manganese,  " 
Sulphur,  " 
Silicon,  " 

Carbon,  " 


0.015 
0.460 
0.032 
0.005 
o.  no 


With  steel,  there  is  practically  no  change  in  tenacity  when  tested 
with  or  across  the  direction  of  rolling.     The  results  of  numerous 


RIVETED    JOINTS.  133 

experiments  indicate  that  the  ultimate  shearing  strength  of  mild 
steel  may  be  taken  generally  as  80  per  cent,  of  the  ultimate  tensile 
strength.  The  allowable  bearing  stress  upon  the  rivet  or  the  sur- 
rounding metal  ranges  usually  from  12,000  Ibs.  to  24,000  Ibs. 
per  square  inch  of  the  projected  semi-intrados  (diameter  x  thick- 
ness), although  considerable  latitude  is  given  this  stress  by  various 
designers. 

2.  WROUGHT  IRON.  —  Iron  plates,  rods,  etc.,  differ  widely  in 
quality,  owing  to  the  nature  of  the  processes  through  which  the 
material  passes  in  manufacture.  In  the  puddling  furnace,  there 
appear  globules  of  wrought  iron  whose  centres  consist  of  excess 
carbon  and  impurities.  These,  when  passed  through  the  rolls,  are 
stretched  into  fibres  whose  outer  surfaces  are  of  soft  iron,  while 
the  interiors  contain  foreign  material  as  above.  As  a  result  of 
this  lack  of  homogeneity,  the  fracture  in  some  cases  appears 
fibrous  ;  in  others,  from  30  to  40  per  cent,  crystalline. 

The  ultimate  tensile  strength  with  the  grain,  i.  e.,  parallel  to  the 
direction  of  rolling,  ranges  from  45,000  to  55,000  Ibs.  per  square 
inch.  Across  the  grain,  this  strength  is  less,  being,  according  to 
Bauschinger's  experiments,  about  78  per  cent,  of  that  with  the  grain. 

With  regard  to  the  shearing  strength  of  wrought  iron,  Professor 
J.  B.  Johnson  *  gives  the  following  summary  of  Bauschinger's 
elaborate  experiments  : 

"  In  general,  we  may  say  that  the  shearing  strength  across  the  thickness  of  the  plate, 
either  with  or  across  the  grain,  is  about  80  per  cent,  of  the  tensile  strength,  while,  il 
the  external  forces  lie  in  the  plane  of  the  plate  and  be  applied  on  the  planes  of  shear 
perpendicular  to  the  plane  of  the  plate,  the  shearing  strength  is  about  the  same  as  the 
tensile  strength.  The  shearing  resistance  on  a  plane  parallel  to  the  plane  of  the  plate, 
is  less  than  45  per  cent,  of  the  tensile  strength. ' ' 

The  allowable  bearing  stress  for  pins  and  rivets  upon  the  surface 
of  the  projected  semi-intrados  is  usually  taken  in  structural  work 
as  12,000  pounds  per  square  inch. 

Despite  the  widespread  introduction  of  steel,  the  use  of  wrought- 
iron  rivets  still  finds  favor,  especially  in  locomotive  work.  It  is 
stated  that,  for  the  sizes  used  in  locomotives,  steel  rivets,  machine- 
driven,  are  not  so  trustworthy  as  first-class  iron  rivets,  the  reason 
given,  being  that : 

"A  rapid  distortion  at  one  operation  of  the  steel  formed  head  is  more  than  liable  to 
reduce  the  tensile  strength  of  the  head.  In  other  words,  were  the  steel  rivet  driven  by 

*"  Materials  of  Construction, "  1898,  p.  486. 


134  MACHINE   DESIGN. 

hand,  the  head  would  be  stronger  than  when  driven  by  machine  and  the  contrary  would 
be  the  case  with  the  iron  rivet.  This  is  well  recognized  in  conditions  where  snap- 
riveting  is  required  and  a  leakage  of  the  rivet  in  service  requires  calking.  Under  these 
conditions  the  steel  rivet  will  stand  more  calking  than  the  iron  rivet,  for  the  reason  that 
the  working  due  to  hard  driving  has  a  refining  effect  on  the  steel  and  seems  to  improve 
its  toughness,  whereas  the  distortion  and  twisting  of  the  grain  of  the  iron  rivet  in  driv- 
ing, seems  to  weaken  instead  of  strengthen  it. "  * 

3.  SHEARING  STRENGTH  OF  RIVETED  JOINTS.  —  For  iron  rivets 
in  steel  plates,  Traill  f  gives  ^  as  the  ratio,  in  single  shear,  be- 
tween the  mean  shearing  strength  per  sq.  in.  of  the  rivet  and  the 
mean  tensile  strength  per  sq.  in.  of  the  plate.     For  steel  rivets  in 
steel  plates,  this  ratio  becomes  ||.     A  rivet  in  double  shear  he  as- 
sumes to  have  1.75  times  its  strength  in  single  shear.     Mr.  J.  M. 
Allen  |   takes  38,000  Ibs.   per  sq.  in.  as  the  strength  in  single 
shear  of  an  iron  rivet  in  steel  plates  and  assumes,  in  double  shear,  an 
increase  of  85  per  cent.,  or  a  total  strength  of  70,300  Ibs.  per  sq.  in. 

4.  COPPER,  when  used  for  the  fire-box  plates  or  stay-bolts  of 
locomotive  boilers,  should  have  a  minimum  tensile  strength  of 
30,000  Ibs.  per  sq.  in.  and  an  elongation  of  at  least  20  per  cent, 
in  a  section  originally  2  ins.  long. 

38.     Rivet-Holes. 

1.  MODERN  PRACTICE,  as  to  punching  or  drilling,  varies  some- 
what, although  the   tendency  toward    the  drilled  hole,   with  its 
greater  accuracy  and  small  liability  to  injury  of  the  metal,  grows 
steadily.     In  boiler-work,  the  U.  S.  Naval  specifications  require  all 
rivet-holes  to  be  drilled  with  the  plates  in  position.     The  rules  of 
the  American  Boiler  Manufacturers'  Association  permit  punched 
holes  in  steel  plate  up  to  ^  inch  thick  ;  in  thicker  plate,  the  holes 
may  be  either  drilled  or  be  punched  and  reamed.     In  stntctural- 
work  the  holes  are  punched,  as  a  rule.     For  field-rivets,  they  are 
drilled  to  templet  or  reamed  with  the  connected  parts  in  place. 
In  hull-work,  rivet-holes  are  generally  punched  from  the  faying 
surfaces  of  the  parts  to  be  connected. 

2.  ULTIMATE  TENSILE  STRENGTH  OF  PERFORATED  PLATES.  — 
If  a  plate  be  perforated  with  a  row  of  holes,  as  for  riveting,  by 
methods,  as  drilling,  which  produce    no    molecular    disturbance 
within  the  metal  immediately  surrounding  the  hole,  leaving  that 

*  Am.  Engineer,  Car  Builder,  and  Railroad  Journal,  May,  1898. 
•f  "  Boilers  :  Marine  and  Land,"  1896,  pp.  44,  45. 
JSibley  College  Lectures,  1890-1. 


RIVETED   JOINTS. 


135 


metal  unchanged  in  structure,  the  plate  will  break,  when  tested  to 
destruction,  in  the  line  of  the  reduced  section  remaining  through 
the  rivet-holes  ;  but  the  ultimate  tensile  strength  of  that  reduced 
section  will  be  found  to  exceed  materially  that  of  the  unperforated 
metal.  In  other  words,  if  two  plates  of  the  same  dimensions  and 
material  be  thus  treated,  one  solid  throughout,  the  other  perforated 
as  above,  they  will  rupture  at  different  total  loads,  but  the  ultimate 
tensile  strength,  per  square  inch,  of  the  net  section  along  the  line 
of  holes  will  be  greater  than  that  of  the  metal  in  the  solid  plate. 
This  apparent  paradox  is  analogous  to  that  which  occurs  with  the 
"grooved  specimens"  discussed  in  §  27.  The  reduction  in  sec- 
tional area  of  metal  along  the  holes  lessens  the  space  for  the  flow 
of  that  metal  and  checks  its  tendency  to  stretch.  Hence,  the  con- 
traction of  area  is  hindered  and  opposition  «to  contraction  gives  in- 
crease in  tensile  strength.  When  the  holes  are  punched,  the  speci- 
men is  still  "grooved"  in  type,  but  the  condition  that  the  metal 
surrounding  the  hole  shall  be  uninjured  by  the  perforation,  holds 
no  longer.  Therefore,  the  gain  in  tensile  strength  is,  in  very  thin 
plates,  nullified ;  and,  in  thicker  plates,  reduced  by  the  loss  in 
quality  of  the  material. 

3.   PUNCHES  AND  DIES.  —  In  punching,  as  shown  in  Fig.  60, 
the  plate  rests  on  a  die  the  bore  of  which  is  conical  with  the  smaller 
diameter    toward    the    punch.      The 
base  of  the  latter  may  be  flat,  givinp- 
a  full  circumference  of  cutting  surface 
in   action   on   contact,  or  the  cutting 
edge  may  be  slanting  or  spiral  (Fig. 
6oa)  so  that,  on  contact,  only  part  of 
the  circumference  is  cutting  and,  for  a 
time,  shearing  proceeds  in  detail. 

With  the  spiral  form,  there  is  a 
saving  in  power  when  the  thickness 
of  the  plate  is  less  than  f  the  di- 
ameter of  the  hole  to  be  punched. 

For  plates  beyond  that  thickness,  the  flat-faced  punch  is  better. 
In  order  to  reduce  the  stress  in  the  plate-metal,  the  die  is  made 
conical,  as  above,  and  its  diameter  is  greater  than  that  of  the 
punch  by  10  to  15  per  cent.  The  general  practice  is  to  make 
the  diameter  of  the  die  equal  to  that  of  the  punch,  plus  o.i  to  0.3 
times  the  thickness  of  plate. 


FIG.  60. 


136  MACHINE    DESIGN. 

The  punch  is  subjected  to  crushing  stress.  The  resistance  to 
punching  may  be  taken  generally  as  that  of  shearing  a  section 
equal  to  the  circumference  of  the  hole  multiplied  by  the  thickness 
of  the  plate.  Since  a  punch  cannot  withstand  more  than  the  total 
crushing  force  corresponding  with  its  cross-section,  it  is  apparent 
that  there  is  a  fixed  limit  to  the  thickness  of  plate  which  it  will  pierce. 

4.  EFFECTS  OF  PUNCHING.  —  On  contact,  the  punch  shears  the 
circumference  of  the  blank  to  be  removed,  thrusting,  in  its  ad- 
vance, upon  the  body  of  the  latter  so  that  there  is  not  only  de- 
trusion  but  a  lateral,  plastic  flow  of  a  portion  of  the  metal  of  the 
blank  into  the  walls  of  the  hole.  The  blank,  when  ejected,  is,  as 
the  experiments  of  Townsend  (§31)  show,  no  denser  than  the 
original  plate  but  its  volume  is  less  than  that  of  the  hole. 

The  lateral  flow  produces  molecular  disturbance  within  the 
metal  immediately  around  the  hole,  and  a  portion  of  this  metal 
becomes  dense  and  hard  with  a  decrease  in  ductility  and  rise  in 
elastic  limit.  There  is  also  a  loss  in  ultimate  strength  which  may 
possibly  arise  from  minute  cracks  in  the  affected  metal.  Since  the 
thickness  of  the  plate  determines  the  allowable  pressure  upon  the 
punch,  the  injury  is  less  with  thin  plates.  It  is  also  smaller  with 
ductile  material,  mild  steel  being  stressed  less  than  wrought  iron. 

Some  experiments  indicate  that  the  flow  and  hardening  are 
greater  on  the  die  side  of  the  plate,  while  others  show  that  the  af- 
fected zone  lies  nearer  the  upper  surface.  In  any  event,  the  in- 
jured metal  appears  to  be  included  wholly  within  an  annular  cylin- 
der, Jg  inch  or  less  in  thickness  around  the  hole.  The  remedy, 
therefore,  is  to  punch  the  hole  ^  inch  smaller  in  diameter  than  de- 
sired and  ream  to  finished  size  or  else  to  anneal  the  plate.  Either 
of  these  methods  will  remove  the  ill  effects  of  punching. 

The  loss  of  tenacity  in  punched  plates  not  subsequently  reamed 
or  annealed,  is  with  plates  |  inch  thick  and  upward,  from  i  o  to  25 
per  cent,  in  iron  plates  and  from  10  to  35  per  cent,  in  steel,  the  loss 
in  the  latter  increasing  with  the  thickness.  The  excess  tenacity  of 
a  drilled  plate  is  usually  toto  12  per  cent.,  although  its  maximum 
range  may  be  double  this,  since  this  gain  depends  upon  the  propor- 
tions of  the  "  grooved  "  specimen  and  the  character  of  the  metal. 

5.  DRILLED  HOLES  have  none  of  the  disadvantages  of  those 
made  by  punching.  The  metal  about  the  hole  is  uninjured  since 
there  is  little  pressure  upon  it  and  no  lateral  flow  exists.  The 
blank  is  removed  from  the  hole  in  detail  by  cutting  instead  of  be- 


RIVETED   JOINTS. 


ing  forced  out  bodily  by  pressure  and  shearing.  The  drilled  hole 
should  be  slightly  countersunk  to  remove  the  sharp  edge,  which, 
when  the  joint  is  loaded,  would  aid  in  shearing  the  rivet. 

6.  TESTS  OF  DRILLED  AND  PUNCHED  PLATES. — The  number  of 
such  tests  with  joints,  is  large.  The  following  tables  *  give,  in 
summary,  the  results  of  experiments  by  Mr.  Kirkaldy  to  deter- 
mine the  ultimate  tensile  strength  of  steel  plates  :  (a)  drilled ;  (S\ 
punched;  (c}  punched  and  afterward  annealed.  Plates  12  inches 
wide  were  used.  In  the  J-inch,  i-inch,  and  a  part  of  the  |-inch 
thicknesses,  the  number  and  diameter  of  the  holes  in  each  half  of 
the  specimen  were,  respectively,  6  inches  and  0.79  inch.  In  the  re- 
mainder of  the  |-inch  and  in  the  i-inch  plate,  the  number  and  diam- 
eter were  6  inches  and  i  .08  inches,  respectively.  The  results  were  : 

(^4)  Ultimate  Stress  per  square  inch  of  Gross  Area  at  Holes.  The  stresses  are 
given  in  tons  and  are  calculated  with  reference  to  the  total  sectional  area  of  the  plate, 
including  therein  the  part  removed  by  perforation  : 


Thickness, 

Jin. 

Jin. 

fin. 

I  in. 

Drilled, 

21.90 

19.60 

I9-65 

18.30 

Punched, 
"        and  annealed, 

19.30 

20.15 

16.65 
18.55 

I5.8o 
18.70 

1345 
17.80 

Mean  Stress  in  tons  per  sq.  in.  of  Net  Section  between  Holes  : 


Thickness, 

}in. 

Jin. 

Jin. 

I  in. 

Drilled, 

36.21 

32-44 

31.64 

29.42 

Punched, 

31-94 

27-53 

24.60 

21.02 

"        and  annealed, 

33-41 

30-75 

30.05 

27.82 

Solid  Plate, 

3I-65 

29.15 

29.70 

27.70 

(C)  Stresses  in  per  cent,  per  sq.  in.  of  Net  Section  compared  with  Solid  Plate : 


Thickness, 

}in. 

Jin. 

fin. 

I  in. 

Drilled, 

113.8 

in.  I 

106.4 

106.1 

Punched, 

IOI.O 

94-2 

82.5 

75-8 

"         and  annealed, 

105.6 

105.6 

IOI.O 

100.3 

(D)  Difference  in  per  cent,  between  the  Ultimate  Stress  per  sq.  in.  of  Net  Section 
of  Perforated  and  Unperforated  Plates  : 


Thickness, 

Jin. 

Jin. 

fin. 

I  in. 

Drilled, 

Gain,  13.8 

Gain,  n.i 

Gain,    6.4 

Gain,    6.1 

Punched, 

"            I.O 

Loss,     5.8 

Loss,  17.5 

Loss,  24.2 

"         and  annealed, 

"       5-6 

Gain,    5.6 

Gain,    i.o 

Gain,    0.3 

From  (A}  it  will  be  seen  that  the  punched  plates  have  the  least 
ultimate  strength  and  the  drilled  plates  the  greatest.     (D)  shows, 

*  Merchant  Shipping,  "Experiments  on  Steel,"  1881,  pp.  12-14. 


138  MACHINE   DESIGN. 

for  the  drilled  plates,  a  gain  in  ultimate  strength  over  that  of  the 
solid  plate  of  6.1  to  13.8  per  cent.,  and  a  loss,  in  the  punched 
plates  from  ^-inch  upward,  of  5.8  to  24.2  per  cent.  The  punched 
and  annealed  plates  occupy  an  intermediate  position,  having  a 
gain  which  is  materially  less  than  that  of  the  drilled  plate.  The 
manner  in  which  the  ductility  of  the  steel  was  affected  by  its  treat- 
ment is  indicated  by : 

(£)  Elongation  in  per  cent,  of  Holes  at  Ultimate  Stress: 


Thickness, 

Jin. 

Jin. 

J  in.      ;        i  in. 

Drilled, 

24-3 

37-0 

37-6             33-5 

Punched, 

11.7 

18.5 

II.  i 

4-3 

"         and  annealed, 

27.1 

35-1 

33-o 

29.8 

As  stated  previously,  the  strength  of  a  grooved  specimen  de- 
pends upon  its  form,  the  quality  of  the  metal,  and  the  method  of 
"  grooving  "  or,  in  these  tests,  of  perforation.  Hence  the  results 
given  apply,  quantitatively,  only  to  the  specimens  tested,  although 
the  general  principles  which  are  indicated,  hold  true  in  all  cases. 


\  4.262 


\* 


\-e 


i! 


n  a 


FIG.    61. 

7.  RIVETED  JOINTS  WITH  PUNCHED  OR  DRILLED  HOLES.  —  Joints 
in  which  the  holes  are  punched  or  drilled  give,  under  test,  similar 
differences  in  strength,  although  the  range  of  variation  will  not  be 
the  same  as  in  the  unriveted  plates  since  the  joint  is  a  built-up 
structure  and  the  load  is  transmitted  from  one  plate  to  another  in  a 
complex  manner.  For  example,  in  the  double-butt-strapped  joint 
shown  in  Fig.  61,*  the  plate  and  straps  were  -jV  mc^  thick  and 

*Jour.  Am.  Soc.  Naval  Engineers,  XII.,  p.  4. 


RIVETED   JOINTS. 


139 


had  a  tensile  strength  of  5 5, OCX)  Ibs.  per  square  inch;  the  rivets 
were  |^|  inch  diameter,  and  their  strength  was  40,000  Ibs.,  and 
70,000  Ibs.  per  square  inch  of  section  in  single  and  double  shear, 
respectively.  The  ultimate  strengths  of  the  joint,  with  the  rivet 
holes  made  as  below,  were  : 

Breaking  Load  in  Lbs. 

Holes  punched 261,600 

"  "         and  reamed 286,800 

"      drilled 308,200 


39- 


Boiler-Seams:   Longitudinal,  Circumferential,  and 
Helical. 

In  the  shell  of  a  cylindrical  boiler,  circumferential  or  girth  seams 
are  perpendicular  to  longitudinal  seams,  and  the  latter  are  parallel 
to  the  axis.  Helical,  in  place  of  longitudinal,  seams  have  been 
used  to  a  slight  extent  for  shells,  and  are  employed  in  riveted  pipe. 
In  Fig.  62,  let : 


FIG.  62. 

R  =  radius  of  boiler-shell  ; 
t  =  thickness  of  boiler-shell  ; 

p  =  steam-pressure  per  gauge  ; 

C  =  length  considered  of  circumferential  seam  ; 

L  ==  length  considered  of  longitudinal  seam  ; 

H  =  length  of  helical  seam  equivalent  to  L  ; 

St  =  unit  tensile  stress  on  circumferential  seam  ; 
S/  =  unit  tensile  stress  on  longitudinal  seam ; 
S"  =  unit  tensile  stress  on  helical  seam. 


140  MACHINE   DESIGN. 

Assume  all  joints  as  having  the  full  strength  of  the  plate,  i.  e., 
as  if  welded.  The  total  load  on  the  circumferential  seam  is  that 
on  the  boiler-head,  or  ~R2  x  p.  The  resistance  of  the  entire  seam 
is  the  product  of  its  length,  thickness,  and  the  permissible  unit 
stress,  or  2xR  x  t  x  St,  Equating  the  load  and  resistance  : 


From  equation  (4)  and  Fig.  I  : 

S/=f  =  2S,,  (78) 

i.  e.,  the  longitudinal  have  double  the  unit  stress  of  the  circum- 
ferential seams.      Expressing  C,  L  and  H  in  the  same  units  : 

Normal  load  on  length,  C  =  C.St; 
Normal  load  on  length,  L  =  L.S'  =  2L.St. 

The  normal  load,  N,  on  the  helical  seam  is  the  sum  of  the 
components  of  the  loads  on  seams  C  and  Z,  which  are  normal  to 
seam  H. 

Component  of  C.St,  normal  to  H  =  C.St-cos  a  ; 

Component  of  2L.St,  normal  to  H=  2L.St-sm  a. 
N=  C.St-cos  a  -f  2L.St  sin  a. 

L  C 


.'.N: 

The  unit  tensile  stress  on  the  helical  seam  will  be  equal  to  the 
total  normal  load  on  the  seam  divided  by  the  length  of  the 
latter,  or:  . 

(79) 


If  C=L,  St"=i.sSt; 
if  C=2L,  St"=i.2St; 
if  C=  $L,  St"  =  i.iSt. 

The  stress  on  the  longitudinal  seam  is  28 t  in  all  cases.  It  is 
apparent  that  the  stress  on  the  helical  seam  decreases  as  C  grows. 
If  L  =  o,  the  helical  seam  becomes  circumferential  and  St"  =  St. 
If  C=  o,  the  seam  is  longitudinal  and  St"  =  2St. 


RIVETED    JOINTS. 


141 


The  strength  required  in  the  seam  is  decreased  by  the  helical 
form  but  its  cost  is  increased  by  the  greater  length  of  the  joint  and 
by  the  necessity  for  the  use  in  all  but  small  boilers  of  plates  with 
inclined  sides,  as  shown  in  Fig.  62,  laid  in  circumferential  bands 
or  courses.  This  waste  of  metal  is  avoided  in  Root's  spiral  riveted 
pipe,  which  is  made  of  single  strips,  joined  by  welding  to  any  de- 
sired length  and  wound  and  riveted  helically  to  form  the  pipe. 
The  thickness  of  the  plate  varies  from  No.  28  to  No.  12,  B.  W. 
G.,  and  the  approximate  bursting  pressures  are  given  as  ranging 
from  900  to  1,300  Ibs.  per  sq.  in.  at  3  ins.  diameter  to  1 10  to  335 
Ibs.  at  24  ins.  diameter.  The  pipe  is  used  for  water,  exhaust 
steam,  etc. 

40.     Forms  of  Riveted  Joints. 

The  function  of  a  riveted  joint  may  be  simply  that  of  resisting 
direct  stresses  upon  it,  as  in  structural  work  ;  or  there  may  be 


f\     © 


added  to  this  the  requirement  that  the  joint  shall  be  also  tight 
against  fluid  pressure.  The  latter  is,  in  steam  boilers,  high  and 
internal ;  in  hull  and  gasometer  plating,  moderate  or  light  and 


142  MACHINE   DESIGN. 

external  and  internal,  respectively,  to  the  joint.  The  duty  of  the 
latter  affects  materially  its  proportions. 

The  plates  are,  in  the  simplest  form  of  joint,  united  by  being 
overlapped  and  riveted ;  in  stronger  but  more  complex  forms 
they  abut,  the  seam  being  covered  infrequently  by  one,  but  usu- 
ally by  two,  external  and  internal  butt  straps  or  cover  plates, 
which  are  riveted  to  the  plates  and  to  each  other.  Lap  Joints  are 
shown  in  Fig.  63.  One  plate  rests  upon  the  other  and  rivets  con- 
nect them.  Fig.  64  illustrates  Double- Strapped  Butt  Joints.  In 
this  form,  the  main  plates  do  not  overlap,  but  remain  in  the  same 
plane,  the  straps  being  above  and  below  the  latter.  Fig.  61 
shows  a  similar  joint  with  straps  unequal  in  width ;  Fig.  65  a  Sin- 
gle-Strapped Butt  Joint ;  and  Fig.  66  a  Single-Strapped  Lap  Joint. 

Joints  differ  also  with  regard  to  the  number  and  arrangement 
of  the  rows  of  riveting  which  are  placed  parallel  to  the  plate-edges 
in  a  lap-joint  or  on  each  side  of  the  seam  in  a  butt-joint.  There 
may  be  from  one  to  four  rows,  giving  a  single,  double,  treble,  or 
quadruple-riveted  joint.  In  chain-riveting  (Fig.  63,  b,  d)  the 
rivets  in  adjacent  rows  are  set  one  behind  the  other  on  a  line  per- 
pendicular to  the  seam.  In  staggered  (zigzag)  riveting  (Fig.  63, 
c,  e)  the  rivets  are  en  echelon,  being  placed  on  a  line  which  meets 
the  seam  at  an  angle.  In  both  of  these  forms,  alternate  rivets  in 
the  outer  or  inner  rows  or  in  both  may  be  omitted.  Group  rivet- 
ing, as  shown  in  Fig.  67,  is  sometimes  employed  in  structural 
work.  The  rivets  are  disposed  usually  in  arithmetical  series,  pro- 
ceeding from  the  centre  outward  with  an  increasing  pitch. 

41.     The  Elements  of  a  Riveted  Joint. 

In  order  to  allow  for  the  expansion  of  the  heated  rivet-blank, 
rivet-holes  of  average  size  are  made  -fa  inch  larger  in  diameter 
than  the  rivet  when  cold.  In  calculating  the  strength  of  a  joint, 
the  diameter  of  the  hole,  not  that  of  the  unheated  rivet-blank, 
should  be  considered,  since  the  latter  is  upset  in  riveting  so  that  it 
fills  the  hole  excepting  for  the  slight  contraction  in  cooling.  The 
pitch,  /,  Fig.  63,  a,  is  the  distance  parallel  to  the  seam  between 
consecutive  rivets  in  the  same  row.  Where  alternate  rivets  are 
omitted  in  any  row,  as  in  Fig.  64,  d,  the  pitch  of  the  joint  and  that 
used  in  calculation,  is  the  greatest  pitch  in  the  several  rows,  since 
lines,  as  m-n  and  o-r,  drawn  through  the  centres  of  its  bound- 
ing rivets  and  normal  to  the  seam,  will  include  a  section  of  the 


RIVETED   JOINTS.  143 

joint  which  forms  a  repeating  pattern  throughout  the  whole  extent 
of  the  latter,  so  that  such  a  section  represents  fully  the  construc- 
tion and  strength  of  the  joint. 

The  transverse  pitch,  or  distance  between  the  centre-lines  of 
adjacent  rivet-rows  in  a  direction  normal  to  the  seam,  as  V,  Fig. 
64,  c,  d,  differs  in  magnitude  in  chain  and  staggered  riveting.  The 
diagonal  pitch,  pd,  in  the  same  figures,  is  the  distance  between  the 
centre  of  a  rivet  and  that  of  the  one  nearest  it  diagonally  in  the 


I  Z 

IT  JT  T    TTHT 

\   \    ! 

!      /K    1 

;!  i  <P 

?! 

i  i  A 

(T\        \£gf  (N          '      fK 

f  rt?  i 

6               CD 

E 

~vJ      LJr: 

i    !   V 

i  \   \ 

A  cb  T  ! 

i    V  T    i    i 

FIG.  67. 
/ 

^\ 

FIG.  68. 

| 

1    \ 

V 

1     1 

FIG.  69. 

next  row.  The  margin  is  the  width  of  plate  or  strap  between  the 
centre  of  the  outer  row  of  rivets  and  the  edge,  as  E,  Figs.  63,  a, 
and  64,  c.  The  lap,  in  lap-riveting,  is  the  amount  by  which  one 
plate  overlaps  the  other  ;  in  butt-riveting,  it  is  the  extent  by  which 
the  strap  overlaps  one  plate.  In  both  cases  it  is  equal  to  2E,  plus 
the  distance  between  rivet-rows.  Before  discussing  these  various 
elements  of  the  seam  in  detail,  consider 

i.  THE  MANNER  OF  FAILURE  OF  A  JOINT.  — Take  the  simplest, 
case  —  that  of  the  single  riveted  lap-joint,  Fig.  63,  a.  This  joint, 
when  tested  to  destruction,  may  fail  by  : 

(a)   Rupturing  the  plate  between  the  rivet-holes,  as  in  Fig.  68  ; 

(£)  Shearing  the  rivets,  as  in  Fig.  69 ; 

(c)  Rupturing  the  margin,  as  in  Fig.  70; 

(d)  Shearing  the  margin,  as  in  Fig.  7 1  ; 

(i)  Crushing  the  plate  or  rivet,  as  in  Fig.  72. 

In  staggered  riveting,  rupture  as  in  (a)  may  proceed  along  the 
diagonal  pitches,  if  the  latter  are  weak  as  compared  with  the 
longitudinal  pitch.  The  same  action,  under  the  same  conditions, 
may  take  place  in  chain-riveting  with  alternate  rivets  omitted  in 
the  outer  row.  In  staggered  riveting  with  alternate  rivets  omitted 


144 


MACHINE   DESIGN. 


in  the  outer  row,  as  in  Fig.  73,  (a)  may  occur  along  the  pitch, 
A-D,  or  along  two  diagonal  pitches  and  the  semi-pitch,  as  A-B- 
C-D.  In  double  butt-strap  joints,  (b)  cannot  take  place  unless 
the  main  plate  shears  each  rivet  at  two  sections. 

In  complex  joints,  failure  may  be  due  to  both  shearing  and  rup- 
ture, thus  a  lap-joint  riveted  as  in  Fig.  64,  h  or  k,  may  give  way 


FIG.  70. 


FIG.  71. 


FIG.  72. 


by  shearing  the  rivets  in  the  outer  row  and  tearing  the  plate  along 
the  rivet-holes  of  the  central  row.  Each  form  of  joint  requires 
separate  investigation  with  regard  to  each  possible  manner  of 
failure.  In  design,  the  desire  is  usually  to  make  the  joint,  as 
nearly  as  possible,  equal  in  strength  throughout.  Its  efficiency  is 
measured  by  the  ratio  of  the  tensile  strength  of  the  net  section  of 
plate-metal  left  along  the  line  of  the  greatest  pitch,  as  compared 
with  that  of  a  similar  section,  one  pitch  long,  of  the  solid  plate. 


FIG.  73. 

An  excess  of  strength,  within  reasonable  limits,  in  other  elements 
of  the  joint  is  not  material,  if  that  of  the  net  section  as  above  be 
fully  utilized  and  yet  be  slightly  less  than  those  of  the  seam  in 
other  respects,  so  that  rupture  will  occur  along  that  line,  since, 
especially  in  joints  for  tightness,  an  unnecessarily  wide  pitch  not 


RIVETED   JOINTS.  145 

only  gives  surplus  metal  and  inequality  of  strength  but  adds  to 
the  difficulty  of  making  the  joint  tight. 

2.   RIVET-DIAMETER.  —  In  a  single-riveted  lap-joint,  let : 
d  =  diameter  of  rivet ; 
/  =  pitch  of  rivet ; 
t  =  thickness  of  plate  ; 
5,  =  unit  ultimate  tensile  strength  of  plate  ; 
Sc  =  unit  ultimate  crushing  strength  of  plate  or  rivet ; 
Sa  =  unit  ultimate  shearing  strength  of  rivet. 
Then,  considering  a  section  of  the  joint  one  pitch  wide : 
Tensile  strength,  net  section  of  plate  =  (p  —  d)t •  St ; 
Crushing  strength,  plate  or  rivet       =  d  •  t  •  Sc ; 

red* 

Shearing  strength,  rivet  = •  S  . 

4 
For  equality  of  strength  throughout : 

d-fSe  =  —'St.'.d=^'^-t  =  Ct  (80) 

d-t-Sc  =  (p-d}t-St.'.d=^-^-^p  =  Kp  (81) 

in  which  C  and  K  are  constants. 

It  will  be  seen  that,  for  equal  strength  throughout,  the  'maximum 
permissible  diameter  of  the  rivet  is  fixed  by  the  thickness  of  the 
plate ;  that,  for  that  maximum  diameter,  there  is  but  one  pitch 
which  is  suitable  under  these  conditions ;  and  that,  if  a  less  diam- 
eter than  the  maximum  be  used,  the  pitch,  for  equal  strength, 
changes  with  it. 

Again,  if  the  holes  are  punched,  the  permissible  rivet-diameter 
for  a  given  thickness  of  plate  is  limited  also,  as  stated  previously, 
by  the  ultimate  strength  of  the  punch,  which,  for  crushing,  is 
?r^2/4  •  Sc.  The  minimum  shearing  resistance  of  the  plate  is  the 
area  of  the  sheared  section  x  the  unit  ultimate  shearing  strength, 
or  Tid-t-  St.  Equating  : 

^Sc  =  ^.^.-.</=^<. ;  =  £•/,* 

4  ^e 

in  which  k  is  a  constant. 

In  structural  work,  the  rivet-diameter  is  usually  f  in.  or  |  in. 
With  cylindrical  steam-boilers,  the  shell-diameter,  steam-pressure, 

*Unwin  :   "Machine  Design,"  1901,  I.,  122. 


146 


MACHINE    DESIGN. 


type  of  longitudinal  seam,  and  factor  of  safety  determine  the  thickness 
of  the  shell -sheets.  From  that  thickness,  the  diameter  and  pitch 
for  equal  strength  throughout,  may  be  found  from  formulae  similar 
to  (80)  and  (81).  In  hull-work,  the  diameter  of  the  rivet  varies 
from  \  in.  to  I  \  ins.,  depending  upon  the  thickness  of  the  plating. 
3.  MULTIPLE  RIVETING. — The  efficiency  of  the  single-riveted  lap 
joint  is  but  little  more  than  50  per  cent.,  i.e.,  (p  —  d}t  -± p  /=  0.5, 
about.  Hence,  only  about  one  half  of  the  full  strength  of  the 
connected  plates  is  utilized.  This  seam  is  employed  only  where, 


FIG.  74. 

owing  to  caulking,  corrosion,  or  other  reasons,  a  sheet  relatively 
so  thick  is  used  that  the  fractional  strength,  as  above,  will  suffice 
to  resist  the  load  upon  the  joint. 

Assume  a  single-riveted  lap-joint  just  capable  of  bearing,  with  a 
proper  factor  of  safety,  a  given  load  and  let  it  be  desired  to  aug- 
ment this  load  without  increasing  the  thickness  of  the  plate.  It  is 
evident  that  the  strength  of  the  joint  must  be  made  greater  in  ten- 
sion, shearing  and  bearing  to  resist  stresses  (a),  (^),  and  (e),  disre- 
garding, for  the  time,  the  stresses  (<:)  and  (d}  within  the  margin. 
To  provide  for  the  rise  in  stress  (#),  the  net  plate-section  must  be 
greater,  i.  e.,  there  must  be  a  wider  pitch.  This  extended  pitch 
will,  from  (81)  and  the  increase  in  shearing  load,  (ft),  per  rivet, 
necessitate  a  larger  rivet-diameter.  The  latter,  however,  is  lim- 


RIVETED   JOINTS.  147 

ited,  for  equal  strength,  by  (80)  and,  in  practice,  by  the  growth 
in  the  pressure  required  for  forming  the  rivet-point,  which  pres- 
sure increases  with  the  size  of  the  rivet,  but  is  restricted  by  the 
thickness  of  the  plate.  Again,  the  pitch,  in  steam -joints  is  lim- 
ited by  the  necessity  for  tightness.  For  these  reasons,  multiple 
(double,  triple)  riveting  must  be  adopted  in  such  a  case.  There  is 
a  marked  gain  from  multiple  riveting,  owing  to  the  better  distri- 
bution of  the  material  of  the  joint. 

Graphically,  this  distribution  is  shown  in  Fig.  74,  in  which  the 
boiler  plate  is  assumed,  with  regard  to  shearing  and  tensile  stresses 
only,  to  be  divided  into  tension-links  and  redundant  material,  the 
latter  being  shaded  in  the  diagrams.  The  width,  b,  of  the  link- 
bars  is  so  proportioned  that  the  total  strength  of  the  link  in  ten- 
sion, 2b-t-St,  is  equal  to  the  shearing  strength,  ncl2/^.- Ss,  of  one 
rivet,  the  latter  being  in  single  shear.  To  provide  for  bearing 
stress,  the  width  of  the  link  at  the  head  should  be  I  ^  to  i  ^ 
times  b.  In  (c)  and  (i),  p  and  d  are  the  same,  the  former  be- 
ing relatively  greater  and  the  latter  relatively  less  than  in  (a). 
Hence,  the  net-plate-section,  (p  —  d)t,  and  the  efficiency,  (p  —  d)t 
-r- p-t  are  greater  in  the  double-riveted  joints  and  the  proportion 
of  redundant  material  is  less. 

4.  PITCH. — The  minimum  pitch  permissible  is  governed  by 
several  considerations.  If  the  distance  between  adjacent  edges  of 
rivet-holes,  is  less  than  the  diameter  of  the  rivet,  the  stress  in 
punching  or  the  lateral  pressure  of  the  plastic  rivet-blank  in 
riveting,  may  crack  the  plate  between  the  rivet-holes.  Again, 
the  maximum  diameter  of  the  rivet-point  is  usually  1.75  times 
that  of  the  hole,  so  that  a  pitch  of  two  diameters  gives  barely 
enough  space  for  the  riveting  dies.  In  practice,  the  minimum 
pitch  is  generally  from  2.$d  to  $d  in  various  classes  of  work. 

The  minimum  pitch  permissible  depends  upon  the  service  of 
the  joint.  If  the  latter  is  to  be  steam-tight,  the  pitch  should  be 
equal  to,  or  less  than,  that  demanded  by  equality  of  strength. 
In  such  a  case,  the  steam  tends  to  enter  between  the  laps  or 
straps  and  the  plates  of  a  joint ;  and  the  strip  of  metal  between 
two  rivets  is,  very  approximately,  in  the  condition  of  a  beam  fixed 
at  its  ends  and  loaded  uniformly.  The  maximum  deflection  of 
such  a  beam  is  : 


148 


MACHINE    DESIGN. 


in  which  w=  unit  pressure,  /=  span,  i.  e.,  pitch,  £=  modulus  ol 
elasticity,  and  /  =  moment  of  inertia  of  the  section  of  the  beam. 
Since  the  deflection  thus  varies  as  the  fourth  power  of  the  pitch, 
the  latter,  to  prevent  leakage,  should  be  as  small  as  possible. 

In  structural  riveting,  this  requirement  as  to  fluid  pressure 
does  not  exist,  but  the  rivets  must  not  be  spaced  too  widely  or 
the  joint  may  open  sufficiently  for  moisture  to  enter,  thus  causing 
rusting  and  eventually  bursting  the  joint.  Again,  when  the  joint 
is  in  compression,  the  strip  between  two  rivets  is  essentially  a  col- 
umn and  is,  therefore,  subject 
to  flexure.  In  the  direction  of 
the  stress,  the  pitch  should  not 
exceed,  as  a  rule,  6  inches  or  16 
times  the  thinnest  outside  plate 
connected.  Transversely  to  the 
stress,  the  pitch  may  be  32  to 
40  times  that  thickness. 

5.  DIAGONAL  PITCH.  —  In 
tension -joints,  the  stress  along 
the  line  of  the  pitch,  p,  is  ten- 
sile only,  while  in  the  direction 
of  the  diagonal  pitch,  pd,  there 
are  both  tensile  and  shearing 
components.  Hence,  the  resistance  of  the  metal  along  pd  is,  with 
regard  to  tension  normal  to  the  seam,  less  than  that  of  the  same 
section  if  located  parallel  to  /.  From  Fig.  75,*  we  have: 

Total  load  on  \  pitch,  A-  C  =  W=(p  —  d}t-  St. 

This  load  must  be  borne  also  by  the  metal  along  the  diagonal 
pitch,  A-B.  Resolving  W  parallel  and  perpendicular  to  A-B : 

Shearing  component  of  W  along  A-B      =  (p  —  d}t-  St  •  sin  6  ; 
Tensile  component  of  W,  normal  to  A-B  =  (/>  —  d}t  •  St  •  cos  6. 

The  unit  shearing  stress,  Ss,  on  the  net  section  along  A-B 
will  be  equal  to  the  total  shearing  load  on  that  section,  divided  by 
the  area  of  the  section,  i.  e., 


FIG.  75. 


*  Commander  A.  B.  Canaga,  U.S.N.,/o«r.  Am.  Soc.  Naval  Engrs.,  VIII.,  2. 


RIVETED   JOINTS.  149 

Similarly,  the  unit  tensile  stress,  Sf,  on  the  net  section  along 
A-B  will  be  equal  to  the  total  tensile  load  on  that  section,  di- 
vided by  the  area  of  the  section,  i.  e., 


For  steel  plates,  the  unit  shearing  stress  on  any  section  should 
not  exceed  T8-g-  of  the  unit  tensile  stress.  Hence  : 

St  =  0.8  S/, 

(p-d)t-St-smO      _R     (p-d)t-St-cosd 
(pd-d)t         -*'•       (pd-d)t         ; 

sin  6  =  T87  cos  0;  tan  6  =  0.8  .-.  0  =  38°  40'.  (82) 

Also  : 

tan  6=  V-±-  =  0.8,  .-.  V=  0.4  /.  (83) 

The  value  of  V  depends  thus  upon  that  of  6  and  the  latter  is 
determined  by  the  assumption  that  St  =  0.8  Stf.  As  a  general 
rule,  Traill  takes  the  available  resistance  of  the  metal  along  the 
diagonal  pitch,  for  tension  normal  to  the  longitudinal  pitch,  as  | 
of  that  of  the  same  section  along  the  latter  pitch. 

6.  TRANSVERSE  PITCH.  —  The  value,  V,  of  this  pitch  has  been 
calculated  in  the  preceding  section  for  staggered  riveting  with  no 
rivets  omitted  in  the  outer  row  (Fig.  64  c]  and  for  chain  riveting 
with  alternate  rivets  omitted  in  the  outer  row  (Fig.  64  d~].     When, 
in  staggered  riveting,  alternate  rivets  are  omitted  in  the  outer  of 
several  rows,  the  values  of  Ffor  the  outer  and  the  next  rows  are 
different,  since,  as  shown  in  Fig.  73,  rupture  may  occur  along  the 
pitch,  A-D,  or  along  two   diagonal  pitches  and  a  semi-pitch,  as 
A-B-C-D.     The   calculation  for   the  value  of  Fmust  be  based, 
therefore,  on  an  equality  of  strength  in  these  two  directions.     The 
method  will  be  given  later  in  the  deduction  of  Traill's  formulae. 

In  simple  chain  riveting,  the  minimum  value  of  V\s  fixed  by  the 
same  considerations  which  govern  the  minimum  pitch,  /.  e.,  to  pre- 
vent cracking  the  plate  and  to  provide  room  for  making  the  rivet- 
point,  V,  minimum,  should  not  be  less  than  2d  and  is  preferably 
2.5^/in  boiler-joints  and  ^d  in  structural  work. 

7.  MARGIN  AND  LAP.  —  To  avoid  cracking  the  plate  in  punch- 
ing or  riveting,  the  distance  from  the  nearest  edge  of  the  nearest 
rivet-hole  to  the  edge  of  a  plate  or  strap  should  not  be  less,  as 


150  MACHINE   DESIGN. 

experience  has  shown,  than  the  diameter  of  the  rivet-hole.  The 
margin  is  measured  from  the  centre  of  the  hole.  The  least  value 
of  the  margin  is  therefore  : 

E=i.$d.  (84) 

The  width  of  the  lap  depends  upon  the  form  of  the  joint.  Thus, 
in  Fig.  63  a,  it  is  2E\  in  Fig.  63  b,  2E  -f  V\  in  Fig.  64  k,  2E  -f  2  Vr 
As  noted  previously,  the  rivet  tends  to  rupture  the  margin,  as 
in  Fig.  70,  and  to  shear  it,  as  in  Fig.  71.  In  designing  the  margin 
for  rupturing  stress,  the  portion  of  the  plate  included  between  the 
rivet  and  the  edge  may  be  taken,  approximately,  as  a  rectangular 
beam,  fixed  at  the  ends  and  loaded  in  the  middle,  since  the  rivet 
is  slightly  less  in  diameter  than  the  hole  and  has,  theoretically, 
but  a  line  bearing  on  the  walls  of  the  latter.  For  such  a  beam, 
the  general  formulae  give  : 

M=\-W-l=S'-     and    -  =  ^-, 
'  c  c         6 

in  which  M=  maximum  bending  moment,  W=  total  load,  /  = 
span,  /=  gravity  moment  of  inertia  of  the  cross-section  of  the 
beam,  c  =  distance  of  most  remote  fibre  of  the  cross-section  from 
the  neutral  axis,  b  =  breadth,  and  d=  depth  of  beam.  In  the 
assumed  beam : 

Span  =  diameter  of  rivet  =  d ; 
Breadth  =  thickness  of  plate  =  / ; 

Depth  =  E-dl2  (Fig.  70)  ; 
Distance  c=\  depth  =  \  (E—  dj  2); 


^  _ 

C    ~  O 

Let  F=  factor  of  safety  and  St-^F=  allowable  working  stress. 
Substituting  : 


It  is  assumed  —  necessarily,  but  practically  without  warrant  —  that 
the  load  on  any  pitch-section,  as  m-n-o-r,   Fig.  64  d,  is  divided 


RIVETED   JOINTS.  I5! 

equally  among  the  rivets  in  that  section.     Thus,  in  the  figure  re- 
ferred to,  the  total  permissible  load  on  the  section  is  : 


and,  since  there  are  three  rivets  in  the  section,  the  load  per  rivet  is  : 


3          * 

In  general,  let  n  =  the  number  of  rivets  in  the  section.     Then : 

(p-d}t  St 
n        '  F' 
Substituting  in  (85): 


n         F  S~  F'         6 


which  equation  applies  to  both  lap  and  butt  joints.     In  a  good 
design,  it  gives  a  close  approximation  to  E  =  i.$d,  as  in  (84). 

The  shearing  and  crushing  of  the  portion  of  the  plate  between 
the  edge  and  the  rivet,  as  in  Fig.  71,  remain  to  be  considered. 
For  equal  strength  of  margin  with  regard  to  these  stresses,  we 
have : 

Resistance  to  shearing  =  2  (  £ )/  •  £, ', 

Resistance  to  crushing  =  d- 1-  Sc. 
Assuming  ^,  =  f  <Se  and  equating  : 

£=  1.2$  d. 

Hence,  if,  as  in  (84),  E=  i.$d,  that  width   will   be  more  than 
sufficient  to  withstand  all  stresses  in  the  margin. 

8.  CHAIN  AND  STAGGERED  RIVETING.  —  If  the  diagonal  pitch 
be  properly  proportioned,  there  is,  theoretically,  no  difference  in 
strength  between  chain  and  staggered  riveting,  although  some 
tests  have  shown  a  slight  advantage  in  favor  of  the  former.  The 
practical  advantage  of  staggered  riveting  is  that  pressure  joints 
may  be  made  tighter,  owing  to  the  reduced  width  of  the  lap.  The 


152  MACHINE   DESIGN. 

breadth  of  the  latter  depends  upon  that  of  the  margin,  £,  and  of 
the  transverse  pitch,  V.  In  chain  riveting,  V=  2  to  2.$d  =  mini- 
mum pitch,  / ;  in  staggered  riveting,  as  shown,  V=  o.4p,  theo- 
retically, although  practically  it  is  greater. 

For  example,  in  double-riveted  lap  joints,  Fig.  63  b,  c,  in  boiler- 
work,  with  steel  plates  and  steel  rivets,  with  plate  -thickness,  t=  0.75 
ins.,  rivet-diameter,  d '  =  1.125  ins.,  and  pitch,  p  =  3.30  ins.  : 

Staggered.  Chain. 

E=i.5<J=  1.69  1.69 

r=  1.78  2.75 

2E+  F=Lap=  5.16  6.13 

9.  BUTT-JOINT,  SINGLE  STRAP.  —  This  seam,  Fig.  65,  consists 
essentially  of  two  abutting  lap-joints.  Theoretically,  it  has,  in 
tension  and  shear,  no  more  strength  than  the  latter,  and,  to  resist 
these  stresses  only,  the  strap  need  be  no  thicker  than  the  con- 
nected plates.  Its  practical  advantage  lies  in  the  fact  that  the 
plates  are  in  the  same  plane  and  the  bending  to  which  they  are 
subjected  in  lap-joints  is  largely  removed.  The  tension  on  the 
plates  will,  however,  tend  to  bend  the  strap  ;  and,  for  this  reason, 
the  latter  should  be  thicker  than  the  plates,  the  increase  depend- 
ing upon  the  form  of  the  riveting  but  being,  as  a  minimum,  ^  the 
thickness  of  plate,  when  no  rivets  are  omitted.  The  sole  advan- 
tage of  this  form  of  joint  lies  in  the  resistance  to  bending  stress 
offered  by  the  thick  strap.  Its  relative  cost,  as  compared  with 
that  of  stronger  joints  of  the  double-strap  type,  warrants  its  use  in 
exceptional  cases  only. 

i  o.  BUTT -JOINTS,  DOUBLE  STRAP.  —  The  advantages  of  this 
joint,  Fig.  64,  are  that,  not  only  are  the  connected  plates  in  the 
same  plane,  thus  transferring  bending  stress  from  them  to  the 
straps ;  but  the  rivets,  with  regard  to  the  plates,  are  in  "  double 
shear,"  i.  e.,  neither  plate  can  withdraw  from  the  joint  without 
shearing,  across  two  sections,  each  rivet  passing  through  it.  The 
efficiency  of  each  rivet  is,  therefore,  as  compared  with  the  lap  or 
single  butt-joint,  apparently  doubled  in  shearing,  although,  as  will 
be  shown  later,  the  strength  in  double  shear  is  not  twice,  but  about 
1.75  times  that  in  single  shear. 

The  progressive  increase  of  efficiency  of  this  joint  with  multiple 
riveting,  is  limited  by  the  fact  that  the  resistances  of  the  plate  and 
rivet  to  bearing  stress  are  not  doubled  with  that  to  shearing.  For 


RIVETED   JOINTS.  153 

example,  consider  a  i^-in.  rivet  passing  through  |-in.  steel  plate. 
Take  St  =  44,000  and  Se  =  70,000.  Then  : 

Single  Shear.  Double  Shear. 

Ultimate  bearing  load  =  d  •  t  •  Sc  =  59,o8o  S9,o8o 

"       shearing    "     =-Kd2l^-Ss=  43,736 

"    =  m/l/4- AX  1-75  =  76,538 

In  single  shear,  the  rivet  has  an  ultimate  strength  of  43,736  Ibs.; 
in  double  shear,  of  76,538  Ibs.  The  bearing  strength  is  the  same 
in  both  cases,  leaving,  in  double  shear,  a  surplus  shearing  strength 
of  17,458  Ibs.,  which  is  unavailable,  since  the  limit  in  bearing  has 
been  reached.  The  data,  as  above,  will  be  regarded  simply  as 
an  indication  of  the  principle  involved. 

The  double-strap  joint  has  also,  and  in  greater  degree,  the  ad- 
vantage of  the  single-strap  joint  in  relieving  the  plates  of  bending 
stress.  With  regard  to  tension  and  shear  only,  the  thickness  of 
the  straps  need  be  but  one  half  that  of  each  connected  plate. 
Owing  to  bending  stress,  however,  as  in  the  single-strap  joint,  each 
strap  should  have,  as  a  minimum,  |  the  thickness  of  the  plate, 
when  no  rivets  are  omitted. 

1 1.  BUTT-JOINT,  UNEQUAL  STRAPS. —  The  butt-joint  with  double 
straps  unequal  in  width,  Fig.  61,  is  stronger  than  a  joint  with 
equal  straps  of  the  narrower  width,  owing  to  the  added  rivets  of 
wider  pitch  in  the  outer  row.  A  properly  designed  joint  of  any 
type  is  so  proportioned  as  to  take  full  advantage  of  the  tensile 
strength  of  the  net  section  of  metal  along  the  pitch  section.  In 
double  shear,  the  shearing  resistance,  as  shown,  grows  more 
rapidly  than  the  tensile  and  bearing  resistances  of  the  joint. 
Hence,  by  increasing  the  width  of  the  inner  strap  and  adding  two 
rivets,  doubly  spaced,  as  at  A  and  B,  Fig.  61,  the  length  of  the  net 
plate-section  becomes  p  —  d,  instead  of  pJ2  —  d,  as  at  C-D,  and  the 
bearing  resistance  is  increased  also,  without  adding  more  shearing 
strength  than  that  given  by  one  rivet  in  single  shear.  The  main  pur- 
pose of  this  type  of  joint  is  to  enlarge  the  net  plate-section,  as  at  A-B. 

This  joint  has  met  wide  adoption  in  stationaiy  and  locomotive 
boilers.  It  has  a  practical  advantage  in  that,  as  the  wider  strap 
is  always  placed  inside,  there  is  a  section  of  metal  within  the  shell- 
sheet  and  back  of  the  calking  edge  on  the  outer  strap.  If,  through 
bad  calking,  the  shell-sheet  be  indented  on  the  outside,  the  inner 
strap  acts  as  a  support  instead  of  providing  an  edge  over  which 


154  MACHINE   DESIGN. 

the  shell-sheet  may  bend  and  crack.     The  half-pitch,  at   C-D 
ensures  tightness. 

12.  LAP-JOINT,  SINGLE  STRAP. — This  joint,  Fig.  66,  consists 
usually  of  an  ordinary  single-riveted  lap-joint  with,  on  the  inside, 
a  butt-strap  or  welt-strip  covering  its  whole  length.     There  are 
three  rows  of  rivets.     Those  in  the  centre  pass  through  both  plates 
and  the  strap ;  those  in  one  outer  row  extend  through  the  strap 
and  one  plate ;  and  those  in  the  other  row,  through  the  strap  and  the 
other  plate.     The  pitch  of  the  outer  rows  is  twice  that  in  the  centre. 

This  joint  is  intermediate  between  the  lap  and  butt  types.  Its 
narrow  central  pitch  ensures  tightness  while  the  wide  pitch  of  the 
outer  rows  gives  increased  length  of  net  plate-section.  The  inner 
edge  of  the  main  seam  is  inaccessible ;  but  the  joint  is  stronger 
than  the  lap-form  in  tension  and  shearing  and  the  strap  makes  it 
stiffer  against  bending.  The  strap,  when  below  the  water-line  in 
a  boiler,  prevents  in  a  lap-joint  the  action  known  as  "  furrowing," 
i.  e.,  the  corrosion  in  grooves  of  the  plate-metal  near  the  joint. 

13.  GROUP  RIVETING,  Fig.  67.  — This  form  of  joint  is  applicable 
especially  in  structural  work  for  splicing  narrow  plates,  etc.     The 
stresses  in  the  net  section  of  plate  decrease  from  Row  No.  II.  on- 
ward and,  in  a  lap-joint,  efficiencies  varying  with  the  number  of 
rows  and  ranging  from  80  per  cent,  upward  are  obtained.     The 
rivets  are  disposed  in  groups  according  to  an  arithmetical  series, 
the  number  in  the  rows  being  : 

i,  2,  i  ; 

or»  i,  2,  3,  2,  i  ; 

or,  i,  2,  3,  4,  3,  2,  i,  etc. 

42.     The  Theoretical  Strength  of  Riveted  Joints. 

The  riveted  joint  is  a  structure  whose  character  and  methods  of 
manufacture  forbid  extreme  refinement  of  design.  The  plates  are 
not  only  exposed  in  various  parts  to  direct  tension,  compression, 
and  shear,  and  the  rivets  to  the  latter  two  stresses  in  addition  to  their 
initial  tension  ;  but  there  is  also,  in  service,  bending  action  on  the 
rivets  and  on  the  plates  or  straps.  Even  on  the  assumption  of 
perfect  workmanship  throughout,  the  relation  of  the  various 
stresses,  with  regard  to  any  element  of  the  joint,  is  so  complex 
that  a  fair  approach  to  the  value  of  the  resultant  stress  could  be 
obtained  only  by  intricate  calculation.  Again,  assuming  such  a 


RIVETED   JOINTS.  155 

calculation  as  possible  in  practical  design,  its  results  would  be  af- 
fected materially  by  the  process  of  manufacture  of  the  joint,  which 
process  is  essentially  of  such  a  nature  as  to  exclude  the  accurate 
fitting  and  alignment  which  are  required  for  the  correct  distribu- 
tion of  the  total  load  among  the  rivets,  plates,  and  straps. 

The  many  tests  of  joints  give  information  of  much  value.  That 
information  is,  however,  conclusive  only  in  revealing  the  apparent 
stress  at  which  certain  elements  of  that  particular  joint  yielded. 
The  actual  stress  which  existed  within  those  elements  at  destruc- 
tion is,  owing  to  hidden  components,  unknown  ;  and  the  rearrange- 
ment of  stresses  which  occurs  at  various  stages  of  a  test  renders 
impossible  an  accurate  determination  of  anything  more  than  the 
apparent  load  on  any  element  at  any  time. 

Furthermore,  the  majority  of  published  tests  have  been  made 
upon  thin  plates  which  develop,  as  a  rule,  maximum  ultimate  re- 
sistance ;  the  bulk  of  the  test  specimens  have  been  narrow  sections 
of  the  joint ;  and  the  method  of  testing  is  direct  tension  on  a  plane 
specimen.  In  practice,  on  the  other  hand,  the  plate  is,  in  boiler- 
work,  if  thin,  of  small  diameter  and  great  curvature ;  or,  for  high 
pressures,  may  be  of  large  diameter  and  less  curvature  but  of  maxi- 
mum thickness.  Again,  in  structures,  a  joint  —  for  example,  that 
in  the  web  of  a  plate -girder  —  may  be  in  tension  at  one  end  and  in 
compression  at  the  other  ;  or,  as  in  the  multiple  plate  form  of 
chord  construction,  it  may  present  conditions  which  differ  widely 
from  those  of  the  simple  joint  tested  in  tension. 

While,  therefore,  actual  experiments  upon  joints  give  the  only 
available  knowledge  of  their  final  strength,  the  use  in  designing 
of  the  results  thus  obtained  should  be  governed  by  the  conditions 
of  the  specimen  tested  and  of  the  joint  required.  As  a  rule,  prac- 
tical designing  regards  only  the  simple  stresses  in  plates  and  rivets  ; 
neglects,  except  in  the  added  thickness  of  butt-straps,  the  bending 
action  within  the  joint ;  allows  for  these  omitted  stresses  by  the 
use  of  a  fair  factor  of  safety  ;  and  accepts  the  efficiency  of  the 
joint  as  thus  computed. 

i.  NOTATION.  — In  the  discussion  of  joint-strengths  which  fol- 
lows : 

d  =  diameter  of  rivet ; 

n  =  number  of  rivets  in  the  pitch-section,  i.  e.,  a  strip  of  joint 
of  length  /  ; 


156  MACHINE   DESIGN. 

t  =  thickness  of  plate  ; 
/j  =  thickness  of  single  butt-strap  =  i-|^; 
tz  =  thickness  of  double  butt-strap  =  |7  ; 
p  =  pitch,  longitudinal,  greatest  ; 
pd  =  pitch,  diagonal  ; 

V=  pitch,  transverse,  in  staggered  riveting,  with  no  rivets  omit- 
ted, and  in  chain  riveting,  when  alternate  rivets  are  omit- 
ted in  outer  row  ; 

V^  =  distance  between  outer  and  next  row  of  rivets  in  staggered 
riveting,  when  alternate  rivets  are  omitted  in  outer  row  ; 
E=  width  of  margin  =1.5^; 
c  =  shearing  constant  =  I  for  lap  and  single  butt-strap  joints 

and  1.75  for  double  butt-strap  joints  ; 
R  =  ultimate  resistance  in  tension  of  a  strip  of  solid  plate,  the 

width  of  the  greatest  pitch,  /  ; 
Rt  =  ultimate  resistance,  in  tension,  of  joint  ; 
Rx  =  ultimate  resistance,  in  shearing,  of  joint  ; 
Rc  =  ultimate  resistance,  in  bearing,  of  joint  ; 
Rm  —  ultimate  resistance  of  joint,  with  alternate  rivets  in  outer 
row  omitted,   when  joint  yields  by  tearing  the  plate 
along  the  central  row  and  shearing  one  rivet  in  the  outer 
row  ; 

St  =  ultimate  unit  tensile  stress  of  plate  ; 
St  =  ultimate  unit  shearing  stress  of  rivet  ; 
Se  =  ultimate  unit  bearing  stress  of  rivet  and  plate  ; 
Et  =  tensile  efficiency,  per  cent,  of  joint  =  RJR  X  100  ; 
Et  =  shearing  efficiency,  per  cent.,  of  joint  =  RJR  X  100  ; 
Ec  =  bearing  efficiency,  per  cent.,  of  joint  =  RcjR  X  100  ; 
Em  =  efficiency,  per  cent.,  corresponding  with  the  ultimate  re- 
sistance, Rm,  or  Em  =  RnJR  x  100. 

2.  LAP-JOINT,  SINGLE  RIVETED.  —  Fig.  63  a.     In    this  joint, 
#  =  I.     We  have  : 

Rt=(p-d}t-St't 


p-t-St. 


RIVETED   JOINTS.  157 

For  equal  strength  throughout : 

^•Ss  =  d-t-S,  (88) 

From  (87) : 

p=*jjd+d.  (89) 

From  (88)  : 

'•I '57554  (90) 


(*?) 


100  =  100 


loo  ; 


(Sc     d\ 

=(-.-) 


A  =  #  x  I0°  =  I  V '  -i  )  I0°- 
^  \s*  f/ 

It  will  be  noted  that  (89)  and  (90)  are  derived  by  equat- 
ing the  bearing  strength  of  the  joint  to  its  tensile  and  shear- 
ing strengths.  As  will  be  shown  later,  the  ultimate  compressive 
or  bearing  strength  of  a  rivet  in  its  hole  or  of  the  walls  of  the  hole 
itself,  is  a  somewhat  uncertain  quantity,  since  the  confined  situa- 
tion of  the  metals  restricts  their  plastic  flow.  The  exact  manner  in 
which  the  "  bearing  pressure  "  acts  upon  the  surface  of  the  rivet  or 
of  the  hole  is  unknown.  It  is  assumed,  with  some  warrant,  to  be 
equivalent  to  a  total  pressure  uniformly  distributed  over  the  pro- 
jected semi-intrados,  or  d  x  /.  Owing  to  the  uncertainty  in  this 
matter,  some  designers  assume,  from  experience,  a  ratio  djt  and 
find  p  by  equating  Rt  and  Rt,  thus  : 

Rt  =  Rs=  (p  —  d}t-St  =  0.7854  dz-  St; 


In  this  equation,  t  is  known  from  prior  considerations  ;  d\t  is  as- 
sumed, giving  the  value  of  d ;  St  ISt  is  ascertained  from  tests  of  the 
metals.  The  value  of/  can  be  found,  therefore,  by  substitution. 


158  MACHINE   DESIGN. 

Example:    Steel   plate  and  rivets;   t  =  %  in.;   .£,  =  65,000;  St 
=  o.SSt  =  52,000  ;  Sc  =  70,000. 
From  (90)  : 

70       0.375  21 

d~  V 
From  (89)  : 

/>  =  ~-  x  0.656  +  0.656  =  1.363,  say  1  1  in. 

Substituting  the  values  of  d  and/  in  the  equations  for  efficiencies  : 

Et=  52.27  percent; 
.£  =  52.44  per  cent.  ; 
Ec  =  5  1.39  per  cent. 

Efficiency  of  Joint  =  51.39  per  cent.,  the  least  of  the  three  effici- 
encies, as  above. 

3.  LAP  JOINT,  DOUBLE  RIVETED,  NO  RIVETS  OMITTED.  —  Fig. 
63,  b,  c.     In  this  joint,  n  =2.     We  have  : 

Rt=(p-d}t.St; 


R=p-t-St. 
For  equal  strength  throughout  : 


.'.(p-d}t-St=n-dtSc;  (92) 

n  x  0.7854^5,  *=n-dtS,  (93) 

From  (92)  : 

(94) 


Equation  (93)  gives  equation  (90)  as  before. 

oo,  (95) 


R  (S    0.7854^  ,  ^ 

=  -£*  x  100  =  n(  ^ .     'f]  100,  (96) 

=  §xioo  =  «(|.|)ioo.  (97) 


RIVETED   JOINTS.  159 

Example.  —  Double-riveted  seam,  chain  or  staggered;  steel 
plate  and  rivets;  t  = -^  in.;  St,  Ss,  Sc  are,  respectively,  65,000, 
52,000,  70,000. 

From  (90): 


From  (94): 


—  X  2  x  0.75  +  0.75  =  2.366,  say  2|  in. 


— 

Substituting  in  (95),  (96),  (97): 

Et  =  68.42  per  cent; 
£=  68.01  per  cent; 
E0  =  68.02  per  cent 

Efficiency  of  Joint  =  68.01  per  cent.,  a  gain  of  68.01  —  51.39 
=  16.62  per  cent,  over  the  single-riveted  seam. 

It  will  be  observed  that  equations  (90),  (94),  (95),  (96),  (97) 
are  general. 

The  double-riveted  seam,  with  alternate  rivets  omitted  in  the 
outer  row,  is  not  used  with  lap-joints. 

4.   LAP  JOINT,  TREBLE  RIVETED,  NO  RIVETS  OMITTED,  chain 
or  staggered,  as  in  Fig.  63  d,  e.     In  this  joint,  n  =  3. 

Example.  —  Steel  plate  and  rivets  ;  t==  ^  in.;  St,  Ss,  Sc  are,  re- 
spectively, 65,000,  52,000,  70,000. 
From  (90)  : 

J- 

From  (94)  : 


+        =  3-432,  say 


From  (95),  (96),  (97)  : 


.£,=  76.36  per  cent; 

Et  =  72.22  per  cent; 
Ee=  76.25  per  cent 

Efficiency  of  'Joint  =  72.22  per  cent.,  a  gain  of  72.22  —  68.01  = 
4.21  per  cent,  over  the  double-riveted  seam.     Compare  with 


160  MACHINE   DESIGN. 

5.  LAP  JOINT,  TREBLE  RIVETED,  ALTERNATE  RIVETS  OMITTED 
IN  OUTER  Rows.  —  In  this  case,  the  grouping  of  the  rivets  is  that 
shown,  on  each  side  of  the  seam,  in  Fig.  64,  h  or  k.  In  this  joint, 
0  =  4. 

Example.  —  Data,  the  same  as  in  the  previous  case.  Since  (90) 
does  not  include  n,  we  have,  as  before,  d=  i|  in.  From  (94) : 

70  13        13 

^  =  67  X  4  X  T6  +  16  =  4'3 ' '  say  4* *  in" 

From  (95),  (96),  (97)  : 

Et  =  81.16  per  cent.; 
Es  =  76.74  per  cent.; 
Ee  =  8 1 .42  per  cent. 

With  regard  to  this  form  of  riveting,  a  further  efficiency  must 
be  considered.  Since  there  are  twice  as  many  rivets  on  the  central 
as  on  either  outer  row,  the  net  plate-section  on  the  central  row  is 
less  and  the  plate  might  tear  along  that  line.  Before  total  yield- 
ing can  occur  in  this  manner,  however,  one  rivet  in  the  outer  row 
must  be  sheared  for  each  pitch-section.  Hence,  with  regard  to 
rupture  in  this  manner,  the  total  resistance,  Rm,  of  the  joint  is  equal 
to  that  in  tension  of  the  net  section  along  the  middle  row,  plus 
that  in  shearing  of  one  rivet  in  the  outer  row.  We  have  for  these 
conditions : 

Rt  (central  row)  =  (p  —  2d}t-  St ; 
Rt  (one  rivet,  outer  row)  =  0.7854^  •  St ; 
Rm  =  Rt  +  Ri  =  (p-  2d)t-St  +  0.7854^'  Sf          (98) 
Similarly  to  (95),  etc.,  the  efficiency  under  these  conditions  is : 

R                     \p-2d      St     0.7854^1 
Em  =  -R  x  wo.|t^-  +  3J —  J  100.       (99) 

Substituting  in  (99)  : 

Em=  81.5  per  cent. 

Comparing  this  with  the  efficiencies  deduced  previously,  Effi- 
ciency of  Joint  =  7<5-7/  per  cent.,  a  gain  of  76.74  —  72. 22  =  4. 52 
per  cent.,  by  omitting  alternate  rivets  in  the  outer  rows. 


RIVETED    JOINTS.  l6l 

The  elements  of  the  two  joints  are  with  : 

t     d     11    p  (middle)     p  (outer] 

No  rivets  omitted  \  \\    3  3^  3_7. 

Alt.  rivets  omitted  1  i|    4  2^  4^ 

The  plate-thickness  and  rivet-diameter  are  the  same  in  both 
cases.  In  the  modified  joint,  one  rivet  has  been  added  and  the 
pitch  of  the  outer  rows  made  greater  and  that  of  the  central  row 
less.  The  addition  of  the  rivet  increases  the  strength  in  shearing 
and  bearing,  since  the  outer  pitch  has  not  been  increased  propor- 
tionately. The  extended  outer  pitch  augments  the  net  plate-sec- 
tion and,  hence,  the  tensile  strength.  The  reduced  pitch  and  ten- 
sile strength  of  the  central  row  are  more  than  balanced  by  the 
added  resistance  of  one  rivet  in  shearing  before  rupture  can  occur 
along  that  row.  Hence,  the  modified  joint  is,  in  every  respect,  the 
stronger.  Its  only  disadvantage  lies  in  the  lessened  tightness,  due 
to  wider  pitch,  on  the  outer  rows,  to  offset  which  there  is  a  re- 
duced pitch  in  the  centre. 

6.  BUTT- JOINT,  SINGLE  STRAP,  Fig.  65.  — This  joint  is,  in  effect, 
composed  of  two  abutting  lap-joints,  one  between   the  strap  and 
each  plate.      Hence,  with  regard  to  the  plates,  the  methods  of  de- 
sign used  for  lap-joints,  apply.     This  is  true  also  of  the  strap,  since 
the  increased  thickness  given  it  is  intended  solely  to  resist  bending 
stress,  which  stress  analysis  does  not  consider.     Under  these  con- 
ditions, there  is,  theoretically,  no  gain  in  efficiency  over  the  lap- 
joint,  except  that  the  bearing  and  tensile  stresses  in  the  strap  are 
less.      The  increased  strength  against  bending  action  is  more  than 
offset  by  the  additional  cost  of  the  strap  and  of  calking  one  more 
seam.      This  joint,  therefore,  is  seldom  used. 

7.  BUTT-JOINTS,  DOUBLE  STRAPS  OF  EQUAL  WIDTH,  Fig.  64. — 
This  joint  is  the  strongest  form  for  any  purpose.     The  straps,  one 
on  each  side  of  the  plates,  reduce  the  bending  action  to  a  minimum 
and  the  rivets  are  in  double  shear.     The  single-riveted  type,  Fig. 
64  «,  is  seldom  used  for  boiler  work,  since,  with  but  one  row  of 
rivets,  the  latter  must  be,  for  strength,  of  relatively  large  diameter 
and  therefore  so  widely  spaced  as  to  interfere  with  tightness.    The 
efficiency  of  such  a  joint  is  only  about  65  per  cent.,  or  less  than 
that  of  the  double-riveted  lap  form,  with  usual  proportions  in  both 
cases. 


1  62  MACHINE   DESIGN. 

The  butt-joint  with  double  straps  consists  essentially  of  two 
double  shear  joints  with  regard  to  the  plates  and  of  four  single 
shear  lap-joints  with  regard  to  the  straps.  Each  strap  is  assumed 
to  bear  one  half  of  the  total  load  upon  the  plates  and  is,  as  stated 
previously,  made  |  the  thickness  of  the  plate,  as  a  minimum,  when 
no  rivets  are  omitted,  in  order  to  provide  for  bending  stress.  The 
relations  between  the  loads  and  strengths  of  the  plate  and  either 
strap  are  : 

Plate.  Strap. 

Load,                                              I  \ 

Strength,  tensile,                   i  f 

"            shearing,                1.75  I 

"            bearing,                  I  £ 

With  one  half  the  load  of  the  plate,  the  strap  has  five  eighths 
the  strength  of  the  latter  in  tension  and  bearing  and  its  shearing 
strength  exceeds  its  load  in  the  proportion  of  i  to  0.875.  Hence, 
if  the  joint  be  designed  properly  for  the  plates,  its  strength  will  be 
ample  for  the  straps. 

The  general  formulae  deduced  previously  for  lap-joints  were 
founded  solely  upon  the  size  and  grouping  of  the  rivets  with  re- 
gard to  the  seam.  Precisely  the  same  conditions  hold  in  butt- 
joints,  double-strapped,  with  the  additional  consideration  that  the 
factor,  c=  1.75,  is  introduced,  since,  with  regard  to  the  plates, 
the  rivets  are  in  double  shear.  Therefore,  for  the  plates  of  such 
joints,  we  have  : 


Rc=(d-t-Sc}n- 

Rt  =  (0.7854  d2-  5.x  1.75)*; 

R  =-t-S 


r2-5,=  ndt-Sc\ 
whence : 

/  =  -^  •  nd  +  d\ 
^t 


-;  (100) 

-374 


RIVETED   JOINTS.  163 

o;  (95) 


*  - 

-  X  100  =  n          -  -  I00.  (101) 

(97) 

Where  alternate  rivets  are  omitted  in  the  outer  row,  the  plate  may 
tear  along  the  central  row  ;  but,  before  yielding  occurs,  one  rivet, 
in  double  shear,  must  be  sheared  in  the  outer  row.  We  have  for 
these  conditions  : 

^(central  row)  =  (/  —  2d}t-  St  ; 

Rs  (one  rivet,  outer  row)  =  i.^j^d2  •  St  ; 

Rm  =  Rt  +  Ra=(p-  2d)t.  St  + 


From  the  equations  given  above  —  if  the  thickness  of  the  plate 
and  physical  characteristics  of  the  metal  be  known  —  the  diameter 
and  pitch  of  the  rivets  and  the  various  efficiencies  of  any  required 
butt-joint  with  double  straps,  may  be  obtained.  When  alternate 
rivets  in  the  outer  row  are  omitted,  the  butt-strap  must  be  thicker 
than  when  no  rivets  are  omitted,  in  the  ratio  (/  —  d)  H-  (/  —  2d), 
as  will  be  shown  later  in  the  deduction  of  Traill's  formulae. 

The  efficiencies  of  butt-joints,  double-strapped,  with  steel  rivets 
and  plates,  as  computed  by  Traill  *  for  cylindrical  boilers,  with  vari- 
ous thicknesses  of  plates  and  diameters  and  pitches  of  rivets,  are  : 

Single-riveted,  59.35  to  65.00  per  cent. 

Double      "  73-39  "  78.00  "      " 


«           « 

each  alternate  rivet  in  1 
outer  row  omitted        j 

(•  79-68 

"82.32  "      " 

Treble       " 

79.68 

"  82.32  "      « 

"           " 

each  alternate  rivet  in      1 
both  outer  rows  omitted  j 

^83.24 

"  841.66  "      " 

<«           it 

each  alternate  rivet  in 
the  outer  row  omitted 

[84.95 

"      « 

Quadruple  " 

83.24 

«  84.66  "      " 

Boilers:  Marine  and  Land,"  1896,  pp.  306-318. 


i64 


MACHINE   DESIGN. 


Example. —  U.  S.  Cruiser  Raleigh;  diameter  of  cylindrical  boilers, 
14  ft.,  6  ins.;  steam -pressure,  160  IBs.,  gauge;  longitudinal  seam, 
butt-joint,  double-strapped,  treble  riveted,  alternate  rivets  in  outer 
rows  omitted  (Fig.  64  k] ;  St  =  65,000  ;  Se  =  70,000  ;  5s  =  44,000  ; 
factor  of  safety  =  4. 5.  From  the  considerations  as  to  the  shell 
(§  44),  the  plate-thickness,  t=  i-j3g  in.  In  this  joint,  n  =  4. 

From  (100) : 


From  (94)  : 


44    1.374 


1-375 


fins. 


7.298  =  say, 


The  corresponding  particulars  of  this  joint,  as  built,  were  : 
/  =  i \\  in.  ;  d  =  iT5g  in.  ;  /  =  J\  in., 

an  allowance  of  -^  in.  for  corrosion  having  been  made  on  the 
calculated  thickness,  /. 

8.  BUTT-JOINT,  DOUBLE  STRAPS  OF  UNEQUAL  WIDTHS,  Fig.  61. 
This  joint,  as  designed  for  locomotive  boilers,  is  shown  in  Fig.  76. 


i*0 

i 
i 

O 

i  ' 
i 
i 

o*i  o 

•  J" 

\St" 

©*  o 

;*$ 

|    ! 

^s: 


/^\ 


FIG.  76. 

The  rivets  are  I  in.  in  diameter  and  of  wrought  iron.  The  plates 
and  straps  are  of  steel.  The  thickness  of  plates  and  of  outer  strap  is 
|  in.  ;  of  inner  strap,  Jg  in.  Take  S,  =  60,000  and  Ss  =  48,000. 
Disregard  resistance  to  crushing.  In  this  joint,  n  =  3.  Failure 
may  occur  by  : 

(a)  Rupture  of  plate  along  outer  row  of  rivets,     (b)  Shearing 
one  rivet,  outer  row  (single  shear)    and   two   rivets,  inner   row 


RIVETED   JOINTS.  165 

(double  shear).     (V)  Rupture  of  plate  along  inner  row  and  shear- 
ing one  rivet,  outer  row  (single  shear). 
For  these  conditions  : 


Rs=  o.;854^2(i  +  2  x  1. 
Rm=(P~  2d)t-St  +  0.7854^-5.; 
R=p-t-S, 

Equating  Rt  and  Rm  :  d  =  0.995,  Sa7  I  in- 
Equating  Rt  and  Rt  :  p  =  5.52,  say  sj  in. 
The  efficiencies  are  : 

n 

£t  =  -g  X  100  =  81.82  per  cent.  ; 

R 

ha  =  -g  9  x  100  =  82.25  Per  cent.  ; 

zp 

^m  =  R  X  I0°  =  8l-92  Per  cent- 

With  regard  to  crushing,  failure  may  occur  by  : 

(d}  Rupture  of  plate  along  inner  row  and  crushing  one  rivet  in 
outer  row  and  inner  strap  ;  (e)  crushing  two  rivets  in  inner  row 
in  plate  or  outer  strap  and  one  rivet  in  outer  row  and  inner  strap. 

The  total  resistances  of  the  joint  are  : 

For  conditions  (d)  : 


For  conditions  (^)  : 

2(1    X    f)S.  +  (I    X 

Investigation  of  these  resistances  shows  that  Sc  must  have  a 
value  of  about  100,000  Ibs.  per  sq.  in.  in  order  to  make  the  effi- 
ciency of  the  joint  about  equal  to  those  already  deduced.  The 
moderate  value  (70,000)  used  previously  with  steel  rivets  will  not 
serve,  therefore,  in  this  case.  Since  the  destructive  limit  of  metal 
wholly  free  to  flow,  differs  from  that  of  the  same  metal  when 
plastic  flow  is  restricted,  as  in  a  riveted  joint,  considerable  varia- 
tions in  the  value  of  Sc  may  be  expected.  Professor  Kennedy 
recommends  96,000  Ibs.  per  sq.  in.,  and  Mr.  Stoney  50  tons  per 
sq.  in.,  for  the  plates  in  butt-joints,  double-strapped. 


166  MACHINE   DESIGN. 

Failure  of  the  lap-seams  of  the  straps  of  this  joint  may  occur 
(disregarding  crushing  stress),  as  follows  : 
Inner  Strap  : 

(/)  By  shearing  3  rivets  in  single  shear ; 

(gf)  By  shearing   I   rivet  in  single  shear  and  tearing  the  plate 
along  the  inner  row  of  rivets. 
Outer  Strap  : 

(/«)  By  shearing  2  rivets  in  single  shear ; 

(k)  By  tearing  the  plate  along  the  inner  row  of  rivets. 

From  (/)  and  (Ji)  it  is  clear  that,  in  shearing,  the  seam  of  the 
inner  strap  is  necessarily  the  stronger  in  this  form  of  joint.  With 
straps  of  equal  thickness,  this  seam  is  also  the  stronger  with  re- 
gard to  (g)  and  (£).  Hence,  for  equality  in  resistance  to  these  two 
methods  of  failure,  the  thickness  of  the  inner  strap  may  be  made 
less  than  that  of  the  outer,  as  in  Fig.  76. 

The  purpose,  in  extending  the  inner  strap  so  that  another  row 
of  rivets  in  double  pitch  may  be  added,  is  that  the  net  plate-section 
—  which  is  then  taken  along  the  added  row  —  may  be  increased, 
thus  giving  greater  tensile  efficiency.  The  latter,  with  this  type,  is 
relatively  high.  Thus,  the  joint  shown  in  Fig.  76  is,  as  compared 
with  butt-joints  having  straps  of  equal  width,  stronger  than  the 
double-riveted  and  but  little  weaker  than  the  treble-riveted  forms, 
no  rivets  being  omitted  in  either  of  the  latter  cases. 

9.  SINGLE-STRAPPED  LAP  JOINT,  Fig.  66. — The  analysis  of  this 
joint  is  given  briefly  in  Reuleaux's  Constructor*  The  joint  con- 
sists of  an  ordinary  single-riveted  lap-seam  with  an  inside  strap 
riveted  to  the  shell  plates  at,  and  on  each  side  of,  the  seam.  The 
pitch  of  the  outer  rows  is  twice  that  of  the  central  line  of  rivets. 
The  central  rivets  pass  through  the  strap. 

Against  stress  normal  to  the  seam,  three  rivets  act  —  two  in  the 
lap-joint  and  one  passing  through  the  strap.  The  assumption  is  that 
the  total  load,  P,  upon  the  pitch-section  is  divided  equally  among 
the  three  rivets  and  that,  hence,  the  strap  withstands  one  third  of 
that  load  and  the  joint  the  remaining  two  thirds.  Therefore,  if 
the  strap  and  plates  be  of  equal  thickness  and  St  be  the  ultimate 
unit  tensile  stress  in  the  plate  beyond  the  joint,  the  corresponding 
stress  in  the  unperforated  plate,  within  the  joint  and  between  the 
rivet-rows,  will  be  %St  and,  in  the  strap,  ^St.  Again,  although 
the  rivets  at  the  lap-seam  pass  through  the  strap,  the  latter  is,  at 

*Suplee's  translation,  1895,  P-  43' 


RIVETED   JOINTS.  167 

that  seam,  pulled  in  opposite  directions  by  equal  forces  and  hence 
transmits  no  stress  to  the  central  row  of  rivets. 

Assuming  equal  thicknesses  and  tensile  strengths  throughout, 
the  ultimate  unit  resistance  of  the  plate,  within  and  without  the 
joint,  and  of  the  strap  would  be  equal  under  similar  conditions  ; 
but,  in  this  type  of  joint,  the  conditions  are  such  that  the  pitch- 
section  beyond  the  joint  bears  the  total  load,  P,  the  unperfo  rated 
plate  within  the  joint  bears  f  P,  and  the  strap  ^P.  Hence,  with 
equal  thickness,  the  plate  within  the  joint  and  the  strap  —  as  com- 
pared with  the  plate  beyond  the  joint  —  are  equivalent,  respec- 
tively, to  metal,  i  -=-  f  =  |  and  1-7-^=3  times  as  strong.  We 
have,  then,  for  the  ultimate  tensile  resistances  and  efficiencies  : 

R  (plate  beyond  joint)  =  /  •  /  •  St  ; 

Rt  (plate  within  joint)  =  f  (p  —  2d)tSt  ; 

Rt  (strap)  =  3  (p  -  2d)tSf 


E,  (strap)  . 

The  efficiency  of  the  strap-metal  will  depend  upon  its  resistance 
on  the  central  row,  along  which  line  it  will  tend  to  part. 

In  shearing  stress,  in  order  that  the  right  hand  plate  may  with- 
draw from  the  joint,  it  must  shear  one  strap  and  two  lap  rivets, 
all  in  single  shear.  For  the  strap  the  conditions  are  the  same. 
Hence,  taking  St  =  0.8  St  : 

ltd* 


R  ,    xd2 

^-^-loo-l-—  -ioa 

Comparing  the  efficiencies  with  those  of  an  ordinary  double-riveted 
lap-joint,  as  in  (95),  (96)  : 

EI  -^ 

p  —  2d  ndz 

Single-strapped  lap-joint:  f  •*—  -  —  •  100  ;  f  •  —  •  100  ; 

p-d  ,    nd* 

Double-riveted  lap-joint  :  —  —  —  •  100;  f  •  —  •  100. 


108  MACHINE   DESIGN. 

10.  GROUP  RIVETING,  as  shown  in  the  lap-joint,  Fig.  67,  is  an 
arrangement  of  the  rivets  in  an  arithmetical  series,  which  grouping 
—  on  the  assumption  of  an  equal  division  of  the  load  among  the 
rivets  —  gives  a  gradually  reducing  tensile  stress  in  the  plate  from 
one  side  to  the  other  of  the  group.  The  substance  of  the  follow- 
ing analysis  is  taken  from  Reuleaux's  Constructor.* 

Referring  to  Fig.  67,  let  Pbe  the  total  load  on  the  pitch-section, 
p  ;  m,  the  number  of  rivets  in  the  central  row  ;  and  a,  the  pitch  of 
that  row.  Then  p  =  m  x  a.  From  the  properties  of  an  arith- 
metical series,  the  total  number  of  rivets  in  the  group  =  w2.  In 
Fig.  67,  m  =  4. 

(a)  Shearing  and  Greatest  Tensile  Stresses.  —  To  find  the  ratio 
between  pitch,  /,  diameter,  d,  and  thickness,  /,  which  shall  give 
equality  between  the  tensile  strength  of  the  net  plate-section  in  the 
first,  or  outer,  row  and  the  shearing  strength  of  the  joint,  let  St  be 
the  unit  tensile  stress  in  the  plate  beyond  the  joint  and  StT  that  in 
the  outer  row.  Then  : 

Rt  (outer  row)  =  (ma  —  d}t-  Stf; 

R  (joint)  =  »z2-  —  -5. 
4 

Equating  and  taking  Ss  =  O.8S* : 


(So,  C) 


From  which,  /  =  ma  may  be  found. 

(b)  Tensile  Stress  in  any  Row.  —  To  find  the  stress  on  the  net 
plate-section  in  any  given  row,  there  must  be  deducted  —  on  the 
assumption  of  an  equal  division  of  the  load  among  the  rivets  — 
the  fraction  of  the  total  load,  P,  which  is  borne  by  preceding  rivets. 
Thus,  in  Fig.  67,  the  net  plate-section  of  Row  I.  carries  the  full 

p 
load,  P;  that  of  Row  II.,  P  minus  the  load,  — 2,  on  the  single  rivet 

*Suplee's  translation,  1895,  P- 41- 


- d 


RIVETED   JOINTS.  169 

of  Row  I.  ;  that  of  Row  III.,  P  minus  loads  on  Rows  I.  and  II, 


or  ^-2,  etc. 
m 


The  fractions  of  the  total  loads  borne  by  the  net  plate-sections 
of  the  various  rows  will  then  be  : 


P-  III, ^.P-  IV, 

411*  * 


•  P,  etc. 


Let  the  unit  stresses  in  the  net  plate-sections,  beginning  with 
the  outer,  be  S/,  Sta,  Stni,  StIV,  etc.  Then,  equating  the  loads 
and  resistances  : 


P=  (ma- 


Row     I.  : 

Row    II.  : 

m2  -  i 

m2 

T?nw  TTT    • 

m2  —  3 

£\.OW   111*  • 

m2 

m2  —  6 

Row  IV.  : 

(ma-  2d)t-Stn; 


—  •  P=  (ma  - 


;  etc. 


(Si,  Q 


Now,  let  a  bear  such  a  proportion  to  d  that  Str  =  Stn.  To  find 
the  value  of  this  ratio  in  terms  of  m,  equate  the  values  of  P  from 
the  first  and  second  equations,  as  above  : 

(ma  —  d)t  =  (ma  —  2d^t-—l — 


(S2,  Q 


which    equation    holds    only   for   the    condition    that   St*  =  Stn. 
Equating  the  value  of  P  for  each  succeeding  row  with  that  for  the 


first  row  and  substituting  the  value  of  -%  : 
Stm_ttf-$     Stir      m2-6 

-5  -  w^2 '  ^  ~  ^^ ;  3 


ttr  —  10 

m2  —  4 


;  etc. 


With  m  =  4,  these  ratios  are,  respectively,  if,  \%,  and  T6^, 
showing  that,  from  the  second  row  inward,  there  is  a  gradually 
decreasing  stress  in  the  plate. 


17°  MACHINE   DESIGN. 

In  order  to  compare  the  results  for  any  given  ratio  between 
diameter  and  thickness  with  varying  values  of  m,  assume  in  (50,  C) 
any  convenient  value  for  this  ratio,  as  : 


d      5 

=  -=  i. 59i6=  say  1.6 


(53,  C) 


Also,  since  St  is  the  unit  tensile  stress  in  the  unperforated  plate  and 
St*  the  greatest  unit  tensile  stress  in  any  net  plate-section  of  the 
joint : 


EI  (joint)  _--i- 

<VJ       '       St         ma 

Again,  for  the  unit  bearing  stress,  Sb,  we  have : 


(54,  C) 


(55,  C) 
Substituting  various  values  of  m  in  equations  (50,  52,  53,  54,  C)  : 


m  = 

,. 

3- 

4. 

5- 

d\t  = 

ab/= 

a\t  = 

1.6 
2.50 
4.00 
0.80 

1.6 

3.33 
5.32 

0.90 

1.6 
4-25 
6.80 
0.94 

1.6 

5-20 

8.32 
0.96 

These  efficiencies  are  based  upon  the  assumptions  that  the  load  is 
divided  equally  among  the  rivets  ;  that  a  bears  such  a  proportion 
to  d  that  St'=  Stn;  that  S,  =  o.8S/ ;  and  that  df  t  =  1.6. 

In  butt-joints,  with  single  or  double  straps,  there  will  be  two 
groups,  one  on  each  side  of  the  seam.  Such  a  joint  has,  practically, 
a  further  advantage  in  the  increased  thickness  of  the  strap. 

43.     General  Formulae  for  Boiler- Joints. 

The  formulae  deduced  in  this  section  are  given  in  Boilers :  Marine 
and  Land,  by  Thomas  W.  Traill,  F.E.R.N.,  in  Foley's  Mechanical 
Engineers'  Reference  Book,  and  in  Seaton's  Mamial  of  Marine 
Engineering  (1890).  In  the  work  referred  to,  Traill  gives  a  com- 
plete series  of  tables  calculated  from  these  formulae,  from  which  the 


RIVETED   JOINTS.  \-ji 

proportions  of  a  joint  for  any  given  boiler-diameter  and  steam- 
pressure  can  be  selected  at  once  without  preliminary  computation. 
These  tables  are  of  much  value  and  have  met  extensive  use  by 
designers  in  the  United  States  and  Great  Britain.  No  deduction 
of  the  formulae  is  given  in  the  works  noted  above.  That  which 
follows  is,  in  substance,  that  prepared  by  Lieutenant  Commander 
F.  J.  Schell,*  U.  S.  Navy,  for  the  use  of  midshipmen  at  the  U.  S. 
Naval  Academy. 

The  notation  used  by  Traill  is  : 

/  =  pitch  (greatest)  of  rivets  in  inches  ; 

d  =  diameter  of  rivets  in  inches  ; 

c  =  a  shearing  constant  whose  value  is   i  for  lap  or  single 

butt-strap,  and  1.75  for  double  butt-strap  joints  ; 
A  =  area  in  sq.  ins.  of  cross-section  of  one  rivet ; 
;/  =  number  of  rivets  in  section  of  length,  p  ; 
Jo  =  percentage  of  plate  left  between  rivets  in  greatest  pitch  ; 
<jol  =  percentage     of     rivet-section    as    compared    with    solid 

plate  ; 

fi2  =  percentage  of  combined  plate  and  rivet-section  when  alter- 
nate rivets  are  omitted  in  outer  row  ; 
pd  =  diagonal  pitch  ; 
E  =  distance  from  centre  of  nearest  row  of  rivets  to  edge  of 

plate  ; 

V  •=•  transverse  distance  between  rows  of  rivets  in  ordinary  zig- 
zag (staggered)  riveting  and  in  chain  riveting  with  al- 
ternate rivets  omitted  in  outer  row  ; 
V^  =  distance  between  outer  and  next  row  of  rivets  in  zigzag 

riveting  with  alternate  rivets  omitted  in  outer  row  ; 
T  =  thickness  of  plate  in  inches  ; 
T'j  =  thickness  of  single  butt-strap  in  inches  ; 
T2  =  thickness  of  double  butt-strap  in  inches  ; 

i.  ASSUMPTIONS.  —  (a)  That  the  mean  tensile  strength  of  steel 
plate  is  28  tons  per  square  inch  of  net  section ;  (&)  that  the  mean 
shearing  strength  of  steel  rivets  is  23  tons  per  square  inch  of  cross- 
section  ;  (c)  that  a  rivet  in  double  shear  offers  1.75  times  the  re- 
sistance to  shearing  opposed  by  a  rivet  in  single  shear ;  ((£)  the 
bearing  stress  is  not  considered. 

*  Jour.  Am.  Soc.  Naval  Engineers,  IV.,  403. 


172  MACHINE    DESIGN. 

2.  PERCENTAGE  STRENGTH  OF  JOINT.  —  The  net  plate-section 
along  the  greatest  pitch  is  (p  —  d}T;  the  sectional  area  of  the 
same  length  of  solid  plate  is  /  x  T.  Hence  : 

p-d 
100-.  (103) 


The  resistance  to  shearing  offered  by  the  rivets  in  one  pitch 
section  is  23  x  A  x  n  x  c  ;  the  tensile  strength  of  the  solid  plate 
of  length  /  is  28  x  /  X  T.  Hence  : 


Consider  now  the  case  in  which  alternate  rivets  are  omitted  in 
the  outer  row,  as  in  Fig.  73.  In  the  next  row,  the  net  plate- 
section  will  be  (/  —  2d)T  and  ioo-(/  —  2d^jp  will  be  the  per- 
centage strength  of  this  row  as  compared  with  the  solid  plate. 
Suppose,  however,  that  the  plate  tears  along  this  row,  as  at  K. 
Then,  before  total  failure  of  the  joint  occurs,  one  rivet,  for  each 
pitch-section,  must  be  sheared  in  the  outer  row.  The  percentage 
strength  of  this  single  rivet  is,  from  (104),  ^kl  -+•  n.  Hence  : 

|fp  fc-ioo-^  +  l-  (-5) 

The  lowest  of  the  values  obtained  from  (103),  (104),  (105)  is 
the  percentage  strength  of  the  joint.  An  examination  of  these 
equations  shows  that,  for  double-strapped  butt-joints,  so  long  as 
d  is  not  less  than  T,  fi2  is  always  greater  than  fi  or  cjol.  This  is 
also  the  case  with  lap-joints,  so  long  as  d  is  not  less  than 

T  T 


If  x  7854      -64515 

Since  both  of  these  conditions  hold  usually,  the  use  of  formula 

(105)  will  seldom  be  necessary. 

3.  DIAMETER  AND  PITCH. — The  usual  cases  are  : 

(#)  To  find  d  so  that  Jfe  =  %l  (i.  e.,  equal  tensile  and  shearing 

strengths  of  joint),  when  /,  c,  n,  a"nd  T  are  given,  equate  (103) 

and  (104): 

p  —  d  2-i.A-n-c 

Ioo.^-  =  ioo--T.  (106) 


RIVETED   JOINTS.  173 

Substituting  A  =  xd2/^  and  simplifying  : 


(*) ' 

(io6): 


^-2p)-^c~'  (I°7> 

To  find  /,  when  d,  c,  n,  and   T  are  given,  we  have  from 

+  -d.  (108) 


(c]  To  find  d  and  /,  when  n,  c,  T,  and  56  =  <fol  are  known,  we 
have,  from  (103) : 

100 


Substituting  this  value  of/  and  A  =  '- —  = —  •  —  in  (104)  : 

4         74 

100  x  23  x  22  x  d2-n-c 

~  =  7>i  =  7>; 


Substituting  this  value  of  «?  in  (109)  : 


As  a  rule,  it  will  be  found  simpler  to  substitute  the  numerical 
value  of  d,  as  found  from  (no),  in  (109),  thus  obtaining  a  value 
for/  directly,  without  using  equation  (ill). 

4.  DIAGONAL  PITCH  AND  WIDTH  OF  BUTT  -STRAPS.  —  The  resist- 
ing value  of  the  net  plate-section  along  the  diagonal  pitch,  pd,  with 
regard  to  tensile  stress  normal  to  the  joint,  is  usually  —  owing  to 
the  shearing  component  (§  26)  along  the  diagonal  pitch  —  about  | 
of  that  of  the  same  section,  if  located  parallel  to  the  joint,  as  in  the 
pitch,  p.  Hence,  the  diagonal  net  section  should  be  |  longer  than 


174  MACHINE   DESIGN. 

that  part  of  the  longitudinal  section  to  which  it  should  be  equiva- 
lent in  transverse  tensile  strength.  In  any  event,  the  diagonal 
pitch  should  not  be  less  than  that  found  by  the  following  formulae  : 
(a)  Ordinary  Zigzag  Riveting  and  Chain  Riveting  with  Alternate 
Rivets  Omitted  in  the  Outer  Row.  Fig.  64  c,  d.  Reference  to  Fig. 
64  c,  shows  that  the  same  reasoning  applies  to  both  cases,  since, 
in  each,  the  net  section  of  two  diagonal  pitches  must  be  made  equiv- 
alent in  strength  to  the  net  section  contained  in  the  greatest  longi- 
tudinal pitch,  p.  The  liability  of  the  plate  to  tear  along  A-B  and 
B-D  should  be  the  same  as  along  A-D  or  B-F.  The  net  section 
along  A-B-D  is  2(pd  —  d}  Tand  that  along  A-D  or  £-Fis  (p—d]  T. 
Hence  : 


*-•  <«») 

From  the  right-angled  triangle,  A-B-C,  we  have,  for  the  distance 
between  the  rows  of  rivets  : 


10 

The  authors  mentioned  previously  state  that,  for  chain  riveting  the 
distance,  V,  should  not  be  less   than 


and,  as  this  result  is  greater  than  that  obtained  from  (113),  it  is 
the  one  which,  usually,  is  found  tabulated. 

The  distance,  £,  from  the  centre  of  the  nearest  rivet-row,  to  the 
edge  of  plate,  should  not  be  less  than  1.5  d.  Hence,  the  minimum 
lap  of  plates  in  a  lap  joint  or  the  half-width  of  butt-strap  is  : 

2E+  V.  (114) 

(£)  Zigzag  Riveting  with  Alternate  Rivets  Omitted  in  Outer  Rcnv. 
Fig.  73-  The  joint  may  fail  by  rupture  of  plate  along  A-B-C-D 


RIVETED   JOINTS.  175 

or  along  A-D.  For  equality  of  strength,  the  resistances  of  the 
two  net  sections  to  tensile  stress  transverse  to  the  seam,  must  be 
equal.  The  net  section  on  B-C  is  (//2  -  d)T  '•  that  on  A-D  is 
(p  -  d}T-  that  on  A-B  or  C-D  is  (pd  -  d)T.  The  section,  to 
which  the  metal  left  along  A-B  and  C-D  must  be  equivalent,  is  : 


Pd  =  °-lP  +  d>  (IIS) 

In  the  right-angled  triangle,  A-F-E,  the  base,  F-E  =  //4.     For 
the  distance,  Vv  between  the  rows  of  rivets,  we  have  : 


_ 
1-  20 

As  before,  the  lap  or  half-breadth  of  butt-strap  is,  with  two 
rows  of  rivets  : 

2E  +  Vr  (117) 

Since  the  riveting  in  all  ordinary  cases  is  of  the  form  shown  in 
Fig.  64,  c,  d,  or  Fig.  73,  or  a  combination  of  those  forms,  formulae 
(112),  (113),  (i  14),  (115),  (i  1 6)  have  a  general  application.  For 
example,  consider  a  double-strapped  butt-joint,  treble-riveted,  zig- 
zag, with  alternate  rivets  omitted  in  the  outer  row.  The  distance, 
Vv  between  the  outer  and  second  row  is  obtained  from  (i  16)  ;  the 
distance,  V,  between  the  second  and  third  rows  is  obtained  from 
(113);  and  the  half-breadth  of  butt-strap  is  : 

2E+  V^  +  V.  (118) 

5.  THICKNESS  OF  BUTT-STRAPS.  —  To  ensure  strength  and  tight- 
ness, the  aggregate  thickness  of  the  butt-straps  should  be  more 
than  that  of  the  plate,  since  thin  straps  will  bend  and  the  joint 
will  work  and  leak.  For  single  butt-straps,  7i  =  f  Tt  and,  for 


1/6  MACHINE   DESIGN. 

double  straps,   T2  =  f  T,  are  taken  arbitrarily  as  the  minimum 
values  allowed,  when  no  rivets  are  omitted. 

When  alternate  rivets  in  the  outer  row  are  omitted,  the  empiri- 
cal minimum  thicknesses,  as  above,  should  be  increased.  Thus, 
with  regard  to  joints  shown  in  Figs.  64  b,  d,  let  : 

T2  =  thickness  of  each  butt-strap,  no  rivets  omitted  ; 

T2f  =  thickness  of  each  butt-strap,  alternate  rivets  omitted. 

With  no  rivets  omitted,  the  plate  can  tear  from  the  strap  or 
strap  from  plate  in  but  one  way,  i.  e.,  along  the  net  section  of 
length,  p  —  d.  Hence,  the  ratio  of  strap-strength  to  plate- 
strength  is  : 


With  alternate  rivets  omitted,  the  strap  may  tear  from  the  plate 
along  the  inner  and  weaker  half-pitch  line  but  the  plate  cannot  be 
ruptured  along  that  line  without  also  shearing  one  rivet  in  the 
outer  row  for  each  pitch  -section.  Hence,  with  the  previous  thick- 
ness, Tv  the  strap  would  be  weaker  than  the  plate.  The  ratio  of 
strap-strength  to  plate-strength,  with  thickness,  T2f,  is  : 

2Tj(p-2d) 

T(p-d) 
Equating  the  ratios  and  taking  T2  =  ^T: 


(no) 


r      - 


Hence,  when  alternate  rivets  are  omitted,  the  butt-straps  must 
be  thicker  than  when  no  rivets  are  omitted,  in  the  ratio, 

p-d 

p  —  2d 

Under  the  same  conditions,  the  thickness  of  a  single  butt-strap  is 


6.  JOINTS  BETWEEN  PLATES  UNEQUAL  IN  THICKNESS.  —  In  gen- 
eral, it  is  customary  to  proportion  the  joint  as  for  two  plates  of 


RIVETED   JOINTS.  177 

the  smaller  thickness.  If  the  disparity  be  great,  the  proportions 
may  be  a  mean  proportional  between  those  for  the  thick  and  those 
for  the  thin  plate. 

44.     The  Thickness  of  Shell  Sheets. 

The  thickness  of  the  shell  plates  of  a  cylindrical  boiler  depends 
upon  the  diameter,  steam-pressure,  tensile  strength  of  plate,  factor 
of  safety,  percentage  strength  of  longitudinal  joint,  and  allowance 
for  corrosion.  The  shell  is  treated  as  a  "thin  cylinder"  and  its 
thickness  is  governed  by  the  principles  given  in  formulae  (i)  to 
(4),  §i-  Let: 

t=  thickness  of  plate,  ins.; 
r  =  internal  radius  of  shell,  ins.; 
P=  steam  pressure,  gauge,  Ibs.  per  sq.  in.; 
St  =  ultimate  unit  tensile  strength  of  plate,  Ibs.  per  sq.  in.; 
/  =  factor  of  safety  ; 

ty  =  percentage  strength  of  longitudinal  joint  ; 
^/ioo  =  strength  of  longitudinal  joint  as  compared  with  solid 

plate. 

If  the  shell  were  seamless  and  a  factor  of  safety  were  not  used, 
we  would  have  by  (4)  : 

P  x  r  =  t  x  St  and  t  =  —=-  • 
°i 

The  shell,  however,  is  as  strong  only  as  its  weakest  part  —  the 
longitudinal  joint.  The  strength  of  that  joint  is  fi/ioo  times  t. 
Hence,  the  thickness  must  be  increased  in  inverse  ratio  over  that 
required  for  a  seamless  shell  and  for  /  there  must  be  substituted 
/  X  ioo/fi.  Again,  the  working  strength  of  the  plate  is  equal  to 
its  ultimate  strength,  divided  by  the  factor  of  safety.  Therefore 
St  must  be  replaced  by  5,  -T-/.  Making  these  substitutions  ; 

t  x  ioo  / 

jy—  Pxrx^; 

P-r-f 


IOO 


1/8  MACHINE   DESIGN. 

If  the  joint  be  designed,  as  is  usual,  so  that  it  will  yield  along  the 

<y  i  _     » 

net  plate-section  of  greatest  pitch,  we  have,  by  (95),  -—  =^— 
and  the  equation  becomes  : 

P-r-f    _  P-r-f-p 
p-d  (p-d)S*  (122) 

' 


For  any  given  conditions,  the  value  of  ft  is  known  in  close  ap- 
proximation or  can  be  taken  from  Traill's  tables.  This  value,  sub- 
stituted in  (121),  gives  t  at  once. 

The  thickness  may  also  be  computed  from  (122)  by  substituting 
the  value  of/  and  d.  Thus,  assuming  that  the  longitudinal  seam 
is  a  butt-joint  with  double  straps  of  equal  width,  we  have  from 
§42: 

(94) 


Substituting  the  values  of/  and  p  —  d  in  (122)  : 

(I23) 


in  which  n  will  be  known  from  the  type  of  joint  and  Se  and  Se  by 
the  tests  of  the  plate.  To  provide  for  corrosion,  Jg  inch  is  usually 
added  to  the  value  of  /,  as  calculated,  for  the  thick  sheets  of  marine 
boilers. 

45.     The  Stresses  in  Riveted  Joints. 

The  riveted  joint  is  not  homogeneous  and  rigid,  but  is  a  built-up 
and,  under  stress,  a  comparatively  yielding  structure.  The  rivets, 
through  which  the  load  is  transmitted,  are  not  at  first  in  contact 
with  the  walls  of  the  rivet-holes,  and  the  metal  of  both  rivets  and 
plates  is  not  only  elastic  but  will  become,  under  excessive  stress, 
plastic.  "  Lost  motion,"  elasticity,  and  plasticity  cause,  with  in- 
creasing pressure  upon  the  joint,  a  continuous  change  in  the  load, 
form,  and  relative  position  of  each  element  of  the  structure. 


RIVETED   JOINTS. 


179 


Thus,  in  the  lap-joint,  Fig.  77,  when  first  riveted,  the  plates  are 
pressed  together  by  the  axial  contraction  of  the  rivet  in  cooling, 
while  the  radial  shrinkage  of  the  latter  leaves  a  slight  annular  space 
between  its  shank  and  the  walls  of  the  hole.  The  tension  on  the 
plates  forms  a  couple  whose  arm  is  approximately  t.  When  such 


FIG.  78. 


a  joint  is  loaded,  the  couple  tends  to  bring  the  plates  into  the  same 
plane,  thus  bending  the  lap  and  inclining  the  rivet,  as  shown  in 
Fig.  78.  This  action  is  opposed  by  the  resistance  of  the  plates  to 
bending  and  by  their  friction  at  the  contact-surfaces.  When  this 
friction  is  overcome,  the  plates  slip  on  each  other,  the  rivet  bears 
at  diagonal  corners  of  the  hole,  and  crushing  pressure  upon  the 
walls  of  the  latter,  and  shearing  and  bearing  actions  on  the  rivet 
are  added  to  the  tensile  and  bending  stresses  already  existing  in 
the  plates  and  rivets.  With  an  increasing  load,  these  conditions 
grow  in  intensity  but  are  modified  in  their  local  effect  by  the  elas- 
ticity of  the  metal.  Finally,  in  more  or  less  of  the  elements  of  the 
joint,  the  plastic  stage  is  reached  and  the  rearrangement  of  stresses 
becomes  more  marked.  At  any  time  during  these  stages,  failure 
may  occur,  if  any  element  be  strained  beyond  its  ultimate  strength. 


FIG.  79. 


FIG.  80. 


Similarly,  in  the  double -strapped  butt-joint,  Fig.  79,  there  is  at 
first  no  bearing  of  the  rivet-shank  upon  plate  or  straps.  The  gradu- 
ally applied  load  expends  its  force  first  in  overcoming  the  frictional 
resistances  between  the  plates  and  straps  and  between  the  latter  and 
the  rivet-heads.  When  slip  at  these  surfaces  occurs,  the  condi- 
tions are  as  in  Fig.  80.  The  rivet  is  bent,  it  bears  at  one  side  on 
the  plates  and  at  the  other  upon  the  straps,  and  it  is  subjected  to 


1  80  MACHINE   DESIGN. 

double  shear,  while  a  bending  moment,  similar  to  that  in  a  lap- 
joint,  acts  upon  the  straps.  All  stresses  now  prevail  ;  and,  with 
increasing  load,  the  elasticity  and  ultimate  plasticity  of  the  metal 
will  cause,  until  destruction,  a  continuous  change  in  the  stress  upon 
any  given  element  of  the  joint. 

i  .  TENSILE  STRESS  IN  RIVETS.  —  This  stress  is  due  to  the  con- 
traction in  cooling.  Its  magnitude  —  if  the  plates  be  tightly 
clamped  during  riveting  —  depends  upon  the  coefficient  of  linear 
expansion,  the  modulus  of  elasticity,  and  the  temperature  at  which 
riveting  is  completed.  Let  : 

A  =  sectional  area  of  rivet-shank  ; 
/  =  length  of  rivet-shank  ; 
E  =  modulus  of  elasticity  ; 
r  =  difference  between  temperature  of  cold  rivet-blank  and  that 

at  which  riveting  is  completed  ; 
/  =  increase,  total,  in  length  for  change  of  r°  ; 
s  =  increase,  per  unit  of  length,  for  change  of  r°  ; 
St  =  unit  tensile  stress  produced  by  contraction  ; 
a  =  coefficient  of  linear  expansion  for  a  change  of  I  °  F. 
Then: 


St  =  E-s  =  a-r-E*  (124) 

The  total  tensile  load  on  the  shank  =  A  x  St.  Equation  (  1  24) 
shows  that  this  load  is  independent  of  the  length  of  the  shank. 
The  deduction  holds  only  while  St  lies  within  the  elastic  limit  of 
the  metal. 

For  steel  in  general,  a  =  .0000065  and  E=  30,000,000  ;  and, 
for  soft  rivet  steel,  St  at  the  elastic  limit  =  30,000  Ibs.  per  sq.  in. 
These  values,  substituted  in  (124),  give  r=  154°.  In  practice, 
however,  the  range  of  temperature  greatly  exceeds  this.  Hence, 
it  follows  that,  with  good  workmanship,  the  cooling  and  attempted 
contraction  strain  the  shank  considerably  beyond  the  elastic  limit. 

The  actual  tension  in  the  shank  is  uncertain,  since  permanent  set 
is  produced  and  the  elasticity  of  the  metal  is  impaired.  Mr. 
Stoney,  in  experiments  quoted  previously  (§36),  gives  the  contrac- 
tile strength  of  iron  rivets  with  hand-made  points  as  12.32  tons 
per  sq.  in.  of  rivet-section,  at  which  stress  the  points  or  heads 

*Merriman:   "  Mechanics  of  Materials,"  1899,  p.  145. 


RIVETED  JOINTS.  l8l 

flew  off.  He  gives  also,  from  his  experiments,  0.6  as  the  coef- 
ficient of  friction  of  ordinary  steel  plates.  For  the  latter,  with 
rivets  as  above,  the  frictional  resistance  to  slip  would  then  be 
12.32  x  0.6  =  7.39  tons  =  16,553  Ibs.  Per  sq-  in.  of  rivet-section. 
Professor  Bach's  experiments  *  show,  for  good  single  lap-riveting, 
similar  values  ranging  from  14,000  to  25,000  Ibs.  per  sq.  in. 

2.  BENDING  STRESS  ON  RIVETS,  Figs.  77  to  80,  inclusive.  In 
lap-riveting,  this  stress  is  a  maximum  as  soon  as  the  plates  engage 
the  rivet,  which  position  is  approximately  that  shown  in  Fig.  77. 
The  rivet,  in  the  lap-joint,  acts  as  a  cantilever,  the  distance  be- 
tween load  and  reaction  being  t ;  in  the  double-strapped  butt-joint 
this  distance  is  (/  +  T2}/2  and  the  rivet  is  a  simple  beam,  loaded  in 
the  middle.  The  classification  and  distances  are  approximate  and 
must  be  regarded  as  simply  an  indication  of  the  principle  involved. 
Let: 

P=  total  load  on  rivet ; 

/                                                     itd* 
-  =  section-modulus  of  nvet  =  ; 

c  32 

6"  =  maximum  stress,  tensile  or  compressive,  due  to  bending ; 
M=  maximum  bending  moment  ; 


t+T, 


in  butt-joints,  double-strapped  ; 


4 
=  P- 1  in  lap-joints  ; 

S--  =  resisting  moment. 

Equating  the  bending  and  resisting  moments,  we  have  for : 
Lap-joints :     S  = 

Butt-joints :     S  =  SP  ^pr- 

In  the  lap-joint,  as  the  plates  bend,  the  bending  moment  de- 
creases. 

3.  SHEARING  STRESS  ON  RIVETS. — When  failure  by  shearing 
occurs  in  lap  and  single-strapped  butt-joints,  but  one  cross-section 
of  the  rivet-shank  is  sheared,  while,  in  double-strapped  butt- 

*  "  Die  Maschinen-Elemente,"  1901,  p.  170. 


1  82  MACHINE   DESIGN. 

joints,  the  shank  must  be  sheared  in  two  places.  In  the  former 
case,  the  rivet  is  said  to  be  in  single,  in  the  latter  in  double,  shear. 
The  resistance  to  shearing  is  the  product  of  the  area  sheared  by 
the  mean  ultimate  shearing  stress  ;  or,  in  the  case  of  a  rivet, 
7Td?z/4  X  St,  for  each  rivet-section. 

In  double-strapped  joints,  as  shown  in  Fig.  80,  the  shearing 
force,  P,  is  always  approximately  normal  to  the  rivet.  Hence,  the 
shearing  resistance  of  the  latter  is  2(>zY/2/4'  ^.)-  In  the  lap-joint, 
Fig.  78,  as  the  laps  bend,  the  force,  P,  does  not  remain  normal  and, 
hence,  has  both  shearing  and  tensile  components  with  regard  to  the 
axis  of  the  rivet.  The  mean  ultimate  shearing  strength  of  steel 
is  taken  as  0.8  of  its  mean  ultimate  tensile  strength.  Therefore, 
the  division  of  the  force,  P,  in  single  shear,  into  tensile  and  shear- 
ing components  diverts  a  portion  of  it  to  the  stress  against  which 
the  rivet's  resistance  is  greater.  As  a  consequence,  the  ultimate 
strength,  in  joints,  of  a  rivet  in  single  shear  is  to  that  of  one  in 
double  shear,  not  as  1:2,  but  as  4  :  7  or  I  :  1.75,  approximately. 
For  each  rivet  in  a  joint,  then  : 

Ultimate  strength,  single  shear  =  -  •  5  ; 

4 

Ultimate  strength,  double  shear  =  -  •  S  x  1-75, 

4 

in  which  d  is  the  diameter  of  the  shank  and  St  is  the  mean  ulti- 
mate unit  shearing  stress. 

The  shearing  stress  varies  in  intensity  throughout  the  cross-sec- 
tion. In  a  solid  of  circular  section,  as  a  rivet-shank,  the  maxi- 
mum is  %  the  mean  shearing  stress.*  Taking  the  maximum  shear- 
ing unit  stress,  5/max.),  as  ^  of  the  ultimate  unit  tensile  stress, 
St,  the  mean  ultimate  shearing  stress, 


While  this  is  the  theoretical  ratio  between  the  maximum  and  mean 
shearing  stresses  of  a  solid  circular  section,  the  common  practice 
is  to  take  St  =  o.8St  for  steel  rivets,  the  discrepancy,  if  any,  being 
covered  by  the  factor  of  safety. 

4.  BEARING  STRESS  ON  RIVETS  and  on  the  walls  of  rivet-holes. 

*Rankine:  "Applied  Mechanics,"  1869,  p.  340. 


RIVETED  JOINTS.  183 

In  a  new  joint,  the  rivet-shank,  owing  to  contraction  in  cooling,  is 
not  in  contact  with  the  plate,  and,  further,  its  initial  tension  pro- 
duces frictional  resistance  to  movement  between  the  plates,  straps, 
and  rivet-heads.  This  friction,  when  the  joint  is  first  loaded,  re- 
duces the  pressure  upon  the  rivet  and  it  must  be  overcome  wholly 
before  the  full  bearing  stress  can  exist.  In  fact,  if  it  be  assumed 
that  each  rivet  carries  the  same  load,  there  would  be,  in  service 
and  with  the  customary  factor  of  safety,  no  bearing  pressure  what- 
ever upon  the  rivets  of  a  new  joint.  Thus,  taking  the  mean  ulti- 
mate shearing  stress  of  rivet-metal  as  44,000  Ibs.  per  sq.  in.,  the 
factor  of  safety  as  4.5,  the  elastic  limit  as  30,000  Ibs.  per  sq.  in., 
and  the  coefficient  of  friction  of  steel  plates  as  0.5,  we  have,  per 
sq.  in.  of  rivet-section  : 

Allowable  shearing  load  =  44,000  -4-4.5  =  9,778  Ibs.; 

Frictional  resistance  at  elastic  limit  =  30,000  x  0.5  =  15,000  Ibs., 

i.  e.,  even  if  the  elastic  limit  were  not  exceeded,  the  resistance  of 
the  plates  to  slip  would  be  50  per  cent,  greater  than  the  permissible 
shearing  load.  In  view  of  these  considerations,  high  authorities  in 
France  and  Germany  (§46)  contend  that  riveted  joints  should  be 
designed  with  regard  to  their  frictional  resistance  and  not  with 
reference  to  the  ultimate  strength  of  their  elements. 

On  the  other  hand,  owing  to  the  elasticity  of  the  plate,  the  ir- 
regularity of  workmanship,  the  bending  of  plates  or  straps,  and 
their  actual  and  relative  movement,  especially  in  pressure-joints, 
during  expansion  and  contraction,  it  seems  probable  that  frictional 
resistance  is  modified  greatly  in  service.  Furthermore,  experi- 
ment shows  that,  in  multiple  riveted  joints,  the  outer  lines  of  the 
rivets  in  test-specimens  bear  a  wholly  disproportionate  share  of 
the  load,  owing  doubtless  to  the  elasticity  of  the  plate  between 
them  and  the  inner  rows.  Hence,  their  load  probably  exceeds 
the  frictional  resistance  they  produce  and  the  latter  may  be  over- 
come in  detail  throughout  the  joint. 

In  considering  bearing  pressure,  assume  for  simplicity,  as  in 
Fig.  8 1 ,  that  the  rivet  is  incompressible,  that  the  elastic  limit  of 
the  metal  is  not  exceeded,  and  that  the  rivet  axis  remains  parallel 
to  the  walls  of  the  hole.  The  total  load,  P,  upon  the  rivet  will 
force  the  latter  into  the  plate  the  distance,  0-0'=  A- A',  since  the 


1 84 


MACHINE   DESIGN. 


displacement,  parallel  to  the  line  of  action  of  P,  will  be  the  same 
for  all  compressed  parts  of  the  plate  in  front  of  the  rivet.  The 
elasticity  and  reaction  of  the  plate  produce  on  any  element,  B,  of 
the  circumference  a  bearing  pressure,  b,  which  is  a  maximum,  b' ,  at 
C  and  varies  as  the  cos  6  throughout  the  quadrant,  being  zero  at  D. 
The  summation  of  the  vertical  components  of  b  equals  P. 


The  rivet,  however,  is  compressible  and  its  section  under 
pressure  is  no  longer  circular.  Again,  Figs.  78  and  80  show  that 
the  pressure  on  the  axial  plane  is  not  uniform  throughout.  Finally, 
under  excessive  stress,  the  plastic  stage  is  reached  and  the  in- 
tensity and  distribution  of  the  pressure  depend  upon  the  free- 
dom of  flow  of  the  metal.  These  unknown  elements  make  an 
analysis  of  the  problem  impossible  without  assumptions  so  broad 
as  to  render  the  results  valueless.  With  regard  to  an  empirical 
formula,  it  may  be  noted  that,  in  summation  by  the  calculus  of 
the  vertical  components  of  b,  the  normal  pressure  upon  the  ele- 
mentary arc,  ds  =  r'dd,  must  be  considered  and  that  the  radius, 
rf=r  =  dl2,  approximately.  Again,  with  a  given  load,/3,  the 
resulting  unit  bearing  pressure  depends,  in  some  degree,  upon  the 
thickness,  /.  These  conditions  warrant  the  introduction  of  d  and 
t  in  such  a  formula,  the  latter  becoming  : 


P=SC  x  d  x  t, 


(125) 


RIVETED   JOINTS.  185 

in  which  P=  safe  load  on   one   rivet  and  Sc  =  a  mean  working 
bearing  stress  determined  by  experiment.     Professor  Unwin*  says  : 

From  experiments  on  indentation,  it  is  known  that  the  resistance  to  indentation  of  a 
plastic  material  does  not  much  depend  on  the  form  of  the  indenting  body,  but  only  on 
the  projected  area  normal  to  the  direction  of  indentation.  Hence,  it  is  not  an  arbitrary 
rule,  but  one  based  on  experiment,  to  take  the  resistance  to  indentation  of  a  plate  of 
thickness,  /,  by  a  rivet  of  diameter,  d,  to  be  proportional  to  the  projected  area,  d  X  '• 

5.  BENDING  STRESS  IN  PLATES.  —  In  a  lap-joint,  the  stress  will 
be  a  maximum  when  the  parts  are  in  the  position  shown  in  Fig. 
77.  For  example,  in  plate,  A,  there  acts  at  the  left  a  force,  P, 
which  produces  a  direct  unit  tensile  stress,  St,  and,  at  the  right,  an 
opposing  force,  P,  with  leverage,  /,  which  tends  to  bend  the  plate 
and  to  produce  a  further  tensile  stress,  Sb,  in  its  upper  fibres. 
The  breadth  of  the  section  thus  bent  is  p  —  d  and  its  depth  is  /. 
The  stresses  are  : 

Lap-joint  (Fig.  77)  : 

Tensile  load  on  section  =  P\ 
Resistance  of  section  =  S^p  —  d}t  ; 

P 

Equating  load  and  resistance  :  St  =  /v,__^w  ' 

Bending  moment  of  load  =  P  x  t  ; 

(p  -  dy 
Modulus  of  section  =?  -  ^  -  ; 

Resisting  moment  of  section  =  Sb  --  g  -  ; 

6P 
Equating  the  moments  :  Sb  =  /    _  ^.  • 

Total  maximum  unit  tensile  stress  =  St  +  Sb  ; 


Double-strapped  Butt-joint  (Fig.  80)  : 


Tensile  load  on  strap  =  —  ; 


*"  Elements  of  Machine  Design,"  Part  I.,  p.  131, 


1  86  MACHINE   DESIGN. 

Resistance  of  strap  =  S((p  —  d)T2  ; 
Equating  load  and  resistance  :  St  = 

Bending  moment  of  load  = 
Modulus  of  section  =  —  —  g-t-*-  ; 
Resisting  moment  =  Sb  •          6       2  5 

Equating  the  moments  :  Sb  =  ^P-  -,  -  .  /L2  • 
Total  maximum  unit  tensile  stress 


These  calculations  will  be  regarded  as  general,  giving  maximum 
results.  In  lap-joints  especially,  the  moment  of  the  load  is  re- 
duced rapidly  by  the  bending  of  the  plates. 

6.  BEARING,  SHEARING,  AND  TENSILE  STRESSES  IN  PLATES.  — 
The  bearing  pressure  between  the  rivet  and  the  walls  of  the  rivet- 
hole,  is,  of  course,  mutual.  The  metal  in  front  of  the  rivet  is,  as 
indicated  in  §  4  1  ,  in  the  condition,  approximately,  of  a  beam  fixed 
at  the  ends,  with,  in  consequence,  a  shearing  stress  at  the  latter 
since,  at  those  points,  the  stress  due  to  the  resistance  of  the  rivet 
is  communicated  to  the  net  section  of  plate  along  the  pitch-line. 
The  distribution  of  the  tensile  stress  in  this  net  section  is  affected 
by  several  conditions  and  presents  a  complex  problem  which  Mr. 
C.  E.  Stromeyer  *  contends  is  treated  most  adequately  by  regard- 
ing the  metal  surrounding  the  rivet  as  part  of  a  section  of  a  thick- 
walled  cylinder. 

It  is  possible  to  gain  from  experiments  some  knowledge  of  the 
conditions  which  prevail.  Thus,  when  a  rectangular  specimen  of 
unperforated  plate  is  tested  to  rupture,  the  fracture  is  of  crescent 
form  and,  if  the  separated  parts  be  brought  together,  they  will 
touch  at  the  sides,  leaving  a  gap  in  the  middle.  Evidently,  then, 
the  stress  is  a  maximum  in  the  centre  of  the  specimen.  Again, 

*  "Marine  Boiler  Management  and  Construction,  "1893,  P-  Io<>- 


RIVETED   JOINTS.  187 

as  shown  in  §38,  the  perforation  of  a  plate,  as  for  rivets,  causes  a 
restriction  of  the  flow  of  metal,  a  change  in  stress-distribution,  and 
an  increase  in  ultimate  tenacity,  owing  apparently  to  the  partial 
removal  of  stress  from  the  centre  of  the  net  plate-section  to  the 
portions  adjoining  the  holes.  Furthermore,  when  such  a  plate 
forms  part  of  a  loaded  joint,  it  is  the  rivets  which  produce  stress 
in  it.  If  the  plate  be  considered,  very  generally,  as  made  up  of 
simple  beams,  each  loaded  in  the  centre  by  one  rivet,  the  stress 
would  be  a  maximum  at  the  walls  of  the  hole  and  reach  its  mini- 
mum at  the  centre  of  the  net  plate-section. 


46.     The  Friction  of  Riveted  Joints. 

Many  tests  to  determine  the  resistance  to  slip  of  riveted  joints 
of  various  types,  have  been  made  at  the  U.  S.  Arsenal,  Water- 
town,  Mass.,  the  results  of  which  will  be  found  in  the  various 
annual  reports  to  the  Secretary  of  War.  M.  Dupuy,*  also,  has 
conducted  extensive  experiments  with  regard  to  the  magnitude 
and  effect  of  the  friction  of  the  joint.  The  researches  of  Professor 
C.  Bach,  of  Stuttgart,  have  been  exhaustive  and  he  has  presented 
strong  argument  in  favor  of  the  theory  which  bases  the  design  of 
riveted  joints  upon  their  frictional  resistance  alone.  The  review 
of  his  conclusions  which  follows,  has  been  summarized  from  the 
matter,  as  set  forth  in  his  work  on  Machine  Design^ 

The  effect,  upon  the  frictional  resistance,  of  the  temperature,  the 
length  of  the  shank,  the  number  of  rivet-rows,  etc.,  is  considered 
separately.  Unless  otherwise  stated,  the  joint  was  not  calked. 
Consider  : 

i.  THE  TEMPERATURE  AT  RIVETING,  either  cherry -red  or  rose- 
red.  Notation  :  t  =  thickness  of  plate,  d  =  diameter  of  rivet, 
/=  length  of  shank.  One  kilogramme  (kg.)  —  2.20462  Ibs., 
avoirdupois  ;  one  millimetre  (mm.}  ==•  0.03937  in.  ;  one  square 
centimetre  (qcm.)  =  0.155  sq.  in. 

(a)  Lap-joint;  /=  13  mm.,  d  =  19  mm.,  1=26  mm.  The 
lower  (cherry-red)  temperature  gave  sometimes  a  greater  friction 
than  the  higher,  averaging  1,199  to  l>ll$  kS-  Per  4*™-  of  rive* 
cross-section. 

*  An.  d.  Fonts  et  Chauss6es. 

f  "  Die  Maschinen-Elemente,"  1901,  pp.  165-170. 


1 88  MACHINE   DESIGN. 

(d)  Lap-joint  with  inside  and  outside  welt-strips  ;  /=  13  mm., 
d  =  19  mm.,  /=  52  mm.,  t  (each  welt)  =  13  mm.  Owing  to  the 
doubled  length  of  shank,  there  was  given,  at  the  higher  tempera- 
ture, a  greater  friction,  averaging  1,769  to  1,305  kg.  per  qcm.  of 
rivet  cross-section. 

Experiments  by  Considere  confirm  (a)  and  apparently  contradict 
(b\  He  found,  that,  at  a  riveting  temperature  of  600°  to  700° 
C.,  the  friction  reached  a  maximum,  being  then  greater  than  when 
the  rivet  was  at  a  rose-red  heat,  say  1000°  C.  Prof.  Bach  con- 
cludes that  it  is  not  the  temperature  of  the  rivet  at  insertion  which 
is  important  but  that  at  the  moment  of  finishing  the  point.  Also, 
in  machine-riveting,  his  experiments  showed,  that,  within  limits, 
the  friction  increased  with  the  duration  of  the  pressure  upon  the 
rivet.  The  resistance  was  affected  further  by  the  temperature,  at 
finishing,  of  the  portions  of  plate  adjacent  to  the  rivet. 

2.  LENGTH  OF  RIVET-SHANK. — The  shank  of  greater  length 
produced  the  higher  resistance.  Thus  : 

(a)  Lap  joint ;  /=  7.5  mm.,  d=  16  mm.,  1=  15  mm.  Resist- 
ance, 846  kg.  per  qcm.  of  rivet  cross-section. 

Lap  joint ;  /  =  7.5  mm.,  d=  16  mm.,  I  =  31  mm.  Resistance, 
1,037  to  1,1 1 1  kg.  per  qcm.  of  rivet  cross-section. 

(&)  Lap  joint;  /=  13  mm.,  ^=19  mm.,  1=  26  mm.  Resist 
ance,  1,115  kg.  per  qcm.  of  rivet  cross-section. 

Lap  joint;  t=  13  mm.,  ^=19  mm.,  I •=  52  mm.  Resistance, 
1,769  kg.  per  qcm.  of  rivet  cross-section. 

The  slip  with  varying  loads  is  shown  by  the  following  experi- 
ments : 

(a)  Single-riveted  lap-joint;  ^=13  mm.,  d  =  19  mm.,  1—26 
mm.,  pitch  =/  =  48  mm.,  number  of  rivets  =  n  —  3,  diameter  of 
rivet-hole  =  20  mm. 

Load.  Load  on  Rivet  Area.  Slip. 

10,000  kg.  I,1 74    kg.  per  gem.  o 

11,000    "  1,291  "  0.0125  mm. 

15,000   "  1,761  "  o.i  " 

20,000   "  2,348  "  1.175       " 

(fr)  Same  joint  as  (a),  excepting  that  length  of  shank  =  52  mm., 
a  plate,  13  mm.  thick,  having  been  laid  on  each  side  of  the  seam. 

It  will  be  seen  that  the  resistance  of  (&)  was  15,000  kg.,  while 
that  of  (a)  was  10,000;  but  that,  with  (b\  the  slip  increased  far 
more  rapidly,  and,  at  20,000  kg.  load,  was  much  greater. 


RIVETED   JOINTS.  189 


Load.  Load  on  Ri 

15,000   kg.  1,761    kg.  pe 

l6,OOO 


17,000 
18,000 
19,000 
2O,OOO 


i,995 
2,"3 
2,230 
2,348 


SKp. 
o. 

0.004    ' 
0.009 

O.202 

1-255 
1.405 


The  breaking  strengths  of  these  joints  were  : 

Kg.  per  gem.,  Rivet-section. 

(«) 3,522 

(*)  '  •     •     •  3,404 

Prof.  Bach's  conclusions  as  to  the  greater  length  of  rivet-shank 
giving  the  greater  resistance  are,  apparently,  at  variance  with  the 
theory  of  contractile  stresses,  as  given  in  §  45.  Assuming  abso- 
lutely the  same  conditions  throughout,  excepting  dissimilar  aggre- 
gate plate-thicknesses  and  shank-lengths,  the  contractile-stress, 
pressure,  and  frictional  resistance  per  sq.  in.  of  rivet-section 
should  be  the  same  in  all  cases,  since  St  =  a-r-E'm  (124).  The 
explanation  of  this  seeming  discrepancy  lies  probably  in  the  fact 
that,  with  the  shorter  shank,  the  expansion,  while  the  same  per- 
centage of  the  length,  is  a  less  amount  actually ;  and,  therefore, 
in  riveting,  will  be  more  affected  by  the  same  looseness  of  plates 
or  other  defect,  than  the  expanded  length  of  the  longer  shank. 

3.  NUMBER  OF  Rows  OF   RIVETS. — The   frictional    resistance 
to  slip  does  not  increase  proportionately  in  passing  from  single  to 
multiple  riveting,  owing  to  the  fact  that  the  elasticity  of  the  plate 
prevents  the  regular  and  proportionate  distribution  of  the  load 
upon    the  joint     Thus,  in    a    lap-joint,  chain-riveting,    6    rows, 
t=  12  mm.,  d=  19  mm.,  diameter  of  rivet-hole  =  20  mm.,  width 
of  plate  =  1 50  mm.,  in  the  plane  of  the  cross-section  of  the  rivets 
slip,  was  observed  at 

6,000  kg.,  load  in  1st  and  6th  rows. 
8,000  "         "        2d    "     5th     " 
11,000  "         "        3d    "     4th     " 

The  slip,  therefore,  was  greater  in  the  outside  rows,  owing  to  the 
unequal  distribution  of  the  load. 

4.  DOUBLE-STRAPPED  BUTT-JOINTS.  —  The  single-riveted  butt, 
as  compared  with  the  single-riveted  lap-joint,  gives  a  somewhat 
less  resistance.     Thus,  /(plate)  =  13  to  14  mm.,  /(strap)  =  9  mm., 


190  MACHINE   DESIGN. 

d=  19  mm.,  resistance  =  906  kg.  per  qcm.,  while,  in  the  single- 
riveted  lap-joint,  with  t  =  12.5  mm.  and  ^=19  mm.,  the  resist- 
ance =  i, 1 86  kg.  per  qcm.  This  difference  arises  from  the  ab- 
sence of  plate-bending  in  the  butt-joint,  the  plates  and  load  being 
in  the  same  plane,  while,  in  the  lap-seam,  the  eccentricity  of  the 
load,  in  bending  the  plates,  clamps  them  more  closely  and  gives 
greater  friction.  Multiple  riveting,  in  butt-joints,  is  affected  by 
the  elasticity  of  the  plate  in  a  manner  similar  to  that  which  has 
been  described  for  multiple  lap-riveting. 

5.  MACHINE  RIVETING. — In  machine-riveting,  the  magnitude 
of  slip-resistance  depends  greatly  upon  the  duration  of  pressure 
upon  the  rivet.     With  rapid  work,  the  friction  may  be  less  than 
in  hand-riveting.     With  sufficient  pressure  and  duration   the  re- 
verse is  true,  especially  when    thick  plates  and,  consequently, 
large  rivets  are  employed. 

6.  INFLUENCE  OF  CALKING.  —  The  effect  of  calking  is  shown, 
in  detail,  by  the  results,  as  follows,  of  experiments  upon  25  lap- 
joints,  in  each  of  which  /=  12  mm.,  d=  19.5  mm.,  diameter  of 
holes  =  20.5  mm.     The  holes  were  drilled  and  the  joints  hand- 
riveted. 

Plates.  Rivet-Heads. 

(a)         5  Joints.                       Not  Caulked.  Not  Calked. 
(3)         5       "                           Caulked  both  sides. 

(c)  5      "                                  "        one  side.  Calked  one  side. 

(d)  5       "                                  "        both  sides.  "        "      " 

(e)  5       "                                  "           "       "  "      both  sides. 

The  results,  in  kg.  per  qcm.  of  rivet  cross-section,  were  : 

Resistance  to  Slip.  Breaking  Load. 

(«)  88 1  3,397 

(*)  1,238  3,413 

(O  i,327  3,3" 

(d)  1,572  3,178 

(e)  1,617  3,258 

Other  things  being  equal,  a  greater  proportional  advance  in  fric- 
tional  resistance  will  be  made  by  calking  the  heads  of  a  short, 
then  a  long,  rivet,  since  that  resistance  depends  also  upon  the 
length  of  the  rivet-shank. 

7.  RESUME. —  Prof.  Bach's  experiments  show  that,  (#)  in  good 
single  lap-riveting,  there  will  be  a  frictional  resistance  ranging 
from  1,000  to  1,800  kg.  per  qcm.  of  rivet  cross-section,  or  even 


RIVETED   JOINTS.  191 

more,  according  to  length  of  shank  and  width  of  specimen  tested  ; 
(<£)  the  age  of  the  joint  has  an  appreciable  effect  upon  the  amount 
of  resistance  ;  (c)  the  magnitude  of  the  resistance  is  fully  adequate 
to  transmit  the  load  generally  placed  upon  a  riveted  joint ;  (d] 
calking  increases  considerably  the  resistance,  a  fact  which  is  of 
importance,  not  only  in  pressure-joints  but  also  in  structural  work 
in  cases  where  inaccessibility  makes  good  riveting  difficult. 


CHAPTER   IV.* 

RIVETED    JOINTS:    TESTS   AND    DATA   FROM   PRACTICE. 

47.     Tests  of  Multiple-Riveted,  Double-Strapped  Butt-joints. 

The  tests  whose  records  follow  were  conducted  under  the 
supervision  of  the  Ordnance  Department,  U.  S.  Army,  at  the 
Watertown  Arsenal  in  1887,  for  the  Bureau  of  Steam  Engineer- 
ing, U.  S.  Navy.  They  are  of  especial  value,  since  the  specimens 
were  unusually  wide,  the  plates  thick,  and  multiple  riveting  was 
used,  the  conditions  thus  corresponding  with  those  of  boiler-joints 
for  moderate  pressures.  The  plates  were  of  open-hearth  steel 
with  drilled  holes  and  sheared  edges  and  the  joints  were  riveted  by 
steam.  The  strips  tested  to  show  the  quality  of  the  metal  were 
of  the  same  grade,  although  not  from  the  same  sheets,  as  the 
joints.  The  mean  tensile  strength  of  three  such  specimens  for 
each  thickness  was  used  in  computing  the  efficiencies  of  the  joints. 
The  plate -thickness  varied  somewhat  at  different  edges.  After 
testing,  the  rivet  heads  were  planed  from  a  number  of  the  joints, 
the  rivets  driven  out  and  butt-straps  removed,  and  the  elongation 
of  the  rivet-holes  measured.  Owing  to  the  absence  of  tensile 
tests  of  the  unperfo rated  plate,  the  efficiencies  of  joints  Iv  /2,  /3 
were  not  computed. 

The  unequal  distribution  of  the  load  among  the  various  rows 
of  rivets  is  shown  clearly  by  the  elongations  of  the  rivet-holes. 
Thus,  in  the  joint,  B2,  Fig.  82  (f-in.  plate,  |-in.  steel  rivets)  which 
failed  by  rupture  at  50,200  Ibs.  apparent  tension  on  net  plate  sec- 
tion, the  average  elongations  on  the  right  of  the  seam  were,  in  the 
outer  row,  0.284  in.;  in  the  central  row,  0.173  in.;  and,  in  the 
inner  row,  0.054  in.  Again,  the  average  elongation  of  the  two 

*For  the  data  from  practice  given  in  this  chapter,  the  author  is  indebted  to  the 
Bureau  of  Steam  Engineering,  U.  S.  Navy  ;  the  Baldwin  Locomotive  Works  ;  Messrs. 
R.  D.  Wood  and  Company;  J.  M.  Allen,  Esq.,  President,  The  Hartford  Steam  Boiler 
Inspection  and  Insurance  Company  ;  E.  D.  Meier,  Esq.,  of  the  American  Boiler  Manu- 
facturers' Association;  the  Editor  of  the  American  Machinist;  C.  C.  Schneider,  Esq., 
Vice-President,  American  Bridge  Company  ;  the  Bureau  of  Construction  and  Repair, 
U.  S.  Navy  ;  Edwin  S.  Cramp,  Esq.,  Vice-President,  the  William  Cramp  Ship  and 
Engine  Building  Company;  and  W.  Irving  Comes,  Esq.,  Secretary,  the  American 
Bureau  of  Shipping. 

I92 


RIVETED   JOINTS.  193 

end  holes  in  the  outer  row  was  0.31  in.;  that  of  the  middle  hole, 
same  row,  was  0.26  in.  Similar  values  for  the  central  row  were 
0.22  in,  and  0.145  in.;  and,  for  the  inner  row,  0.065  m-  and  0.05  in. 
The  stress  in  the  joint  section  was,  therefore,  greatest  at  the  edges. 


.0    !    0 

iO    O 


FIG.  82. 

As  shown  in  Fig.  82,  the  metal  drew  down  in  thickness,  in  diag- 
onal and  zigzag  lines  between  the  rivet-holes  of  adjacent  rows, 
although  the  space  thus  traversed  was  greater  than  that  along  the 
pitch-line.  All  riveting,  through  two  butt-straps,  was  zigzag  with 
no  rivets  omitted. 

In  the  tables  which  follow,  tests  No.  905  and  909  are  sample 
records  of  the  strips  tested  to  show  the  quality  of  the  metal.  The 
succeeding  tables  give  tension  tests  of  metal  from  the  fractured 
ends  of  the  joints,  the  tests  of  the  joints,  and  data  as  to  the  mode 
and  appearance  of  fracture.  The  widths  of  the  various  classes  of 
joint-specimens  tested,  were  : 

A,  B,  K,  20  ins.;  D,  17  ins.;  E,  16.5  ins.;  G,  15.75  ins-;  -^ 
20.12  ins.;  /,  14.39  ins. 


TEST  No.  905. — SPECIMEN  C2. — THICKNESS,  FIVE  EIGHTHS  INCH. 
Gauged  length,  15  inches  ;    cross  section,  12"  X  •^>39//  >   area,  7-668  square  inches. 


Applied  Loads. 

In  Gauged  Length. 

Remarks. 

Total. 

^inT"6 

Elongation. 

Set. 

Pounds. 

Pounds. 

Inches. 

Inches. 

7,668 

I.OOO 

0.0000 

o.oooo        Initial  load. 

38,340 

5,000 

.0017 

o.oooo 

76,680 

10,000 

.0042 

o.oooo 

115,020 

15,000 

.0065 

o.oooo 

^ 

153,360 

20,000 

.0089 

o.oooo 

M 

161,028 

21,000 

.0094 

^" 

168,696 

22,000 

.0098 

n 

176,364 

23,000 

.0103 

- 

184,032 

24,000 

.0108 

^b 

191,700 

25,000 

.0112 

—  .0001 

6 

194,000 

.0113 

^             "3 

196,000 

.0115 

«      i 

198,000 

*OIl6 

v~            ^ 

200,000 

.0118 

lo 

2O^  OOO 

.OI2O 

_  -s 

204,000 

.0123 

o>         So 

206,000 

.0125 

Tt-        'O 

208,000 

.0127 

&f^ 

210,000 

.0130 

212,000 

•OI33 

^  ^  oo 

.214,000 

.0136 

S5^? 

2l6,OOO 

.0140 

3  °°.  - 

2l8,OOO 

.0144 

*     £5-0 

220,000 

.0150 

%~  c  's 

222,000 

28,950 

.0154 

Elastic  limit.                            %  .  2   tj 

224,000 

.0162 

-    rt     c 

226,000 

.0170 

V*  •»  JL 

228,000 

.0183 

^  c§    « 

230,000 

.0213 

%•       ^ 

232,000 

.0277 

•  it  *S 

234,000 

.0480 

%"  ^  £ 

236,000 

•0995 

^  ^ 

237,708 

31,000 

•2175 

1  '«  u' 

245,376 

32,000 

•23 

V  a  € 

253,044 

33,000 

•25 

°1    o*  g 

260,712 

34,000 

.28 

v"  <»  -2 

268,380 

35,ooo 

•31 

g  £   >. 

276,048 

36,000 

•33 

-  •*  S 

283,716 

37,000 

•37 

^  ||  ^ 

291,384 

38,000 

•41 

**'  ^)   "•> 

299,052 

39,000 

•45 

ui    't  ^ 

306,720 

40,000 

•5o 

0    X  ^ 

314?  3&^ 

41,000 

•54 

"•2    ^       1) 

322,056 

42,000 

•59 

81  vS  3 

329,724 

43,000 

.66 

"a     ^   2 

337,392 

44,000 

•71 

C     ^7  **^ 

345,060 

45,000 

.78 

*S  2  "o 

352,728 

46,000 

.86 

Cgo 

360,396 

47,000 

•95 

•2  ^^    ^ 

368,064 

48,000 

1.07 

M    ^     S 

375,732 

49,000 

I.2I 

§  I  §: 

383,400 

50,000 

1.47 

s  <  < 

391,068 

51,000 

1.58 

398,736 

52,000 

i.  80 

406,  404 

53,ooo 

2.08 

414  072 

54,000 

2.98 

414,800 

0 

54,ioo 

0 

3-42 
o 

5-52 

Tensile  strength. 
=  36.8  per  cent. 

(p.  194) 


RIVETED   JOINTS. 


195 


TEST  No.  909. — SPECIMEN  Fs.— THICKNESS,  SEVEN  EIGHTHS  INCH. 
Gauged  length,  15  inches;  cross  section,  8.5io//  X  $&l"  >  area,  7.378  square  inches. 


Applied  loads.                        In  gauged  length. 

Remarks. 

Total.            Per  square       Elongation. 
|        me  . 

Set. 

Pounds. 

Pounds. 

Inches. 

Inches. 

7,378 

I,OOO 

O.OOOO 

0.000 

Initial  load. 

36,890 

5,000 

.OO2O 

O.OOO 

73,780 

10,000 

.0045 

o.ooo 

110,670 

15,000 

.0070 

o.ooo 

147,560 

20,000 

.0097 

o.ooo 

154,930 

21,000 

.0103 

162,316 

22,000 

.0108 

169,694 

23,000 

.0115 

172,000 

.0120 

174,000 

.0122 

176,000 

.0124 

I78.0OO 

.0127 

l8o,OOO 

.0130 

l82,000 

•0134 

184,000 

.0137 

l86,000 

.OI42 

188,000 
190,000 

25,750 

.0147 
•0153 

Elastic  limit 

192,000 

.0165 

194,000 

.0182 

196,000 

•1775 

206,584           28,000 

•23 

213,962           29,000 

.26 

221,340           30,000 

.28 

228,718           31,000 

•32 

236,096 

32,000 

•35 

243,474 

33,000 

.38 

250,852 

34,ooo 

•43 

258,230 

35,ooo 

•47 

265,608 

36,000           .52 

272,986 

37,000           .57 

280,364 

38,000 

.63 

287,742 

39,ooo 

.69 

295,120 

40,000 

•74 

302,498 

41,000 

.84 

309,876 

42,000 

•92 

317,254 

43,000 

I.OI 

324,632 

44,000 

1.16 

332,010 

45,000 

1.28 

339,388 

46,000 

1.47 

346,766 

47,000 

1.67 

354,H6 

48,000 

1.98 

361,524 
365,700 
0 

49,000 
49,570 

0 

2.48 
3-3* 

5.31 

Tensile  strength. 
=  35.4  per  cent 

Elongation  of  inch  sections:  .17",   .20*    22",  .25",  .29",  -36",  •49//,  *Ml 

VJ",   .29",   .25*,  .21",  .\l",  .12". 

Area  at  fracture,  6.43"  X  &*  =  3-73  square  inches.     Contraction   494  per  cent 
Appearance  of  fracture,  silky,  lamellar.     Fracture  open  at  the  middle,  .40"  ;  edges 
closed. 


196 


MACHINE   DESIGN. 


TABLE  XLI. 

TESTS  OF  RIVETED  JOINTS  FOR  BUREAU  OF  STEAM  ENGINEERING, 


, 

I 

Sectional  Area  of 
Plate. 

i 

"8 

8 

Style  of  Joint. 

fa 

Size  and  Kind  of  Rivets 
and  Holes. 

I 

1 

1* 

Gross. 

Net. 

fc 

Inch. 

Sq  inches.  &7  inches. 

910 

912 

J 

(Double  riveted  ;  dou- 
ble butt  straps  £  in. 
thick  ;  3  in.  pitch. 

I! 

}\  inch  steel  rivets; 
||     inch    drilled 
holes. 

f  13.22 

13.08 
I  12.41 

10.12 
IO.OI 

9-50 

913 
914 

915 

Bi 
B2 

Treble  riveted  ;    dou- 
-    ble  butt  straps  £  in. 
thick  ;  3T9^  in.  pitch. 

II 

)£  inch  steel  rivets  ; 
|f     inch     drilled 
holes. 

'12.81      10.31 

-    12.69        10.21 
12.691      10.21 

Ql6 

Dj 

1  Double  riveted  ;  dou- 

$   j  ~)  i  inch  steel  rivets  ;  I 

(  14.671      10.09 

917 

D2 

ble  butt  straps  f  in. 

|    1  \      i  A   inch    drilled 

-^   14.646     10.07 

918 

Ds 

thick  ;  3|  in.  pitch. 

[   I     J      holes. 

(14.705    io.ii 

919 
920 
921 

1 

1  Treble  riveted  ;    dou- 
ble butt  straps  J  in. 
thick  ;  4T9^  in.  pitch. 

£      ^|  I   inch  steel   rivets  ; 
•     \      I      i-j-1^   inch    drilled  . 
|    i  J       holes.                        ; 

14.322      10.63 
-     14438      10.72 
.  14.256      10.58 

Leavitt  joint  ;   double 

butt  straps  ;    one  of 

usual  width  for  dou- 

ble   riveting    and  £ 
inch  thick  ;  other,  f 

3  plates  ;    ITV  inch 
iron    rivets  ;       I  \ 

922 

G, 

inch   thick    and   ex- 

| 

in.    drilled  holes. 

I3.78I 

10.93 

923 

G2 

t-    tended     far    enough 

£ 

}-2       plates;         i} 

j    13.852      10.985 

924 

G8 

on  each  side  to  re- 

£ 

in.     iron     rivets  ; 

I3.74I 

10.90 

ceive  five  additional 

ij     inch     drilled 

rivets   in   two  rows. 

holes. 

Pitch  of  double  rivet- 

ing  on    inner   rows, 

2|  inch. 

,' 

1 

1   Leavitt    joint  ;     same 

925 

926 
927 

H; 

arrangement  as  in  G 
series     except     that 
wide  butt  strap  has 
six    rivets    on    each 
side  beyond   narrow 
strap.     Pitch  of  dou- 
ble     riveting,       7.\ 

1 

3     plates  ;     I     inch 
iron   rivets  ;     ly1^ 
in.    drilled  holes. 
2    plates  ;     I  \    inch 
iron     rivets  ;      I  J  j 
inch  drilled  holes. 
1 

13.252 

•!  12.776 
1  12.81 

10.537 
10.154 
10.186 

inch. 

Leavitt    joint  ;     same 

f 

arrangement  as  in  G 

928 

i, 

series  except  that  the 
five  rivets  in  ends  of 

A 

T|  inch  iron  rivets  ; 

8.287 

6.820 

929 

i 

wide  butt  strap  are 

•  K 

\-      i      inch      drilled 

•(      8.21  1 

6-755 

930 

i» 

differently      spaced. 

S 

holes. 

8.28 

6.81 

Pitch  of  double  riv- 

eting on  inner  rows, 

2£  inch. 

931 

KI 

(Treble  riveted  ;    dou- 

|   ;  )  f   inch    iron  rivets;     ("12.36        9.94 

932 
933 

i 

ble  butt  straps  \  in. 
thick  ;  3T9^  in.  pitch. 

-     |      I      ||     inch     drilled 
Jyj      holes. 

4  12.93  i  I0-4o 
(  12.98      10.44 

*  No  figures  given  because  no  tests  were  made  of  this  thickness  of  metal  for  tensile 
strength. 


RIVETED   JOINTS. 

TABLE  XLI. — Continued. 

UNITED  STATES  NAVY  DEPARTMENT. 


I97 


^8* 

Maximum  Stress  on  Joint  per  Square  Inch. 

Bearing 

Shearing: 

Sal 

Surface 
of  Rivets. 

Area  ot 
Rivets. 

«5  «5 

p* 

H 

Tension 
on  Gross 
Section 
of  Plate. 

Tension 
on  Net 
Section 
of  Plate. 

Compression 
on  Bearing 
Surface  of 
Rivets. 

Shearing 
on  Rivets. 

Efficiency 
of  Joint. 

Sq.  inches. 
6.72 
6.64 
6.30 

Sq.inches. 
12.46 
12.46 
12.46 

Pounds. 
53.710 
53.710 
53.710 

Pounds. 
42,860 
40,960 
42,720 

Pounds. 

tss 

55,800 

Pounds. 
84,320 
80,690 
84,  140 

Pounds. 

45,470 

43,ooo 
42,540 

Percent. 
79.8      a 
76.2     b 
79-5      c 

8.01 
7-93 
7-94 

15-34 
15-34 

15-34 

53.710 
53.710 
53.7'Q 

43,460 
40,390 
44,290 

54,040 
50,200 
55,050 

69,560 
64,630 
70,790 

36,320 
33,4io 
36,640 

80.9     d 
75-2     e 
82.5     f 

8.25 
8.23 
8.27 

15-96 
15-96 
15.96 

5LI90 
51,190 
5LI90 

35,l8o 
36,190 
35,780 

51,1.50 
52,640 
52,050 

62,560 
64,410 
63,630 

32,340 
33,2io 
32,970 

68.7     g 
70.7     h 
69.9      i 

10.15 
10.23 

I9-5J 
19-51 

5LI90 
51,190 

37,910 
38,400 

51,080 
51,720 

53,500 
54,190 

27,830 
28,420 

74-1      J 
75.0     k 

10.10 

19-51 

51,190 

37.950 

51,130 

53,560 

27,730 

74-1      1 

16.30 
16.38 
16.26 

28.00 
28.00 
28.00 

5LI90 
51,190 
51,190 

40,8lO 
41,740 
40,120 

51,460 
52,640 
50,580 

34,500 
35,300 
33,910 

20,090 
20,650 
19,690 

79-7    m 
81.5     n 
78.4     o 

14-045 
13.548 

30.41 
30.41 

53,710 
53,710 

42,820 
45.300 

53,860 
51,000 

40,410 
42,720 

18,660 
19,030 

79-7     P 

84-3    q 

I3.576 

30.41 

53.710 

46,070 

57,940 

43.470 

I9,4io 

85.8      r 

8.057 

1  8.06 

* 

42,250 

51,330 

43,450 

19,380 

*        s 

7-994 

1  8.06 

* 

40,800 

49,590 

41,910 

18,550 

*        t 

8.05 

1  8.06 

* 

40,720 

49,520 

41,890 

18,670 

*        u 

7-773 
8.08 
8.ii 

15-34 
15-34 
15-34 

53.710 
53.710 
53.710 

43,600 
43,260 

43,000 

54,220 
53,780 

53.46o 

69,720 
69,220 
68,820 

35,130 

36,460 
36,390 

81.2     v 
80.5     w 
80.1     x 

Figures  in  heavy-faced  type  indicate  manner  of  failure. 

For  explanation  of  reference  letters  in  last  column,  see  next  page. 


I98  MACHINE   DESIGN. 

MODE  OF  FRACTURE  AND  APPEARANCE  OF  FRACTURED  SURFACES. 

a.  Sheared  the  rivets  in  one  plane  in  Plate  A  ;  started  a  fracture  at  side  of  one  rivet 
hole  in  outside  row  of  riveting. 

b.  Fractured  Plate  A  along  outside  row  of  rivet  holes.      Appearance  of  fractures, 
silky,  lamellar. 

c.  Fractured  Plate  A  along  outside  row  of  rivet  holes  ;  sheared  ( double  shear )  six 
rivets  in  Plate  B.     Appearance  of  fractures,  silky,  slight  lamination. 

d.  Fractured  Plate  A  along  outside  row  of  rivet  holes.    Appearance  of  fractures,  silky. 

e.  Fractured  Plate  A  along  outside  row  of  rivet  holes.     Appearance  of  fractures, 
silky,  slightly  lamellar. 

f.  Fractured  Plate  A  along  outside  row  of  rivet  holes.      Appearance  of  fractures, 
silky,  lamellar. 

g.  Fractured  Plate  B  along  outside  row  of  rivet  holes  ;  tore  apart  from  one  edge.   Frac- 
tures also  started  in  Plate  A  at  opposite  edge.      Appearance  of  fractures,  silky,  lamellar. 

h.  Fractured  both  plates  along  outside  row  of  rivet  holes.  The  separation  of  Plate 
A  was  complete  ;  Plate  B  fractured  through  four  sections.  Appearance  of  fractures, 
silky,  slightly  lamellar. 

i.  Fractured  both  plates  along  outside  row  of  rivet  holes.  Plate  B  did  not  separate 
at  one  edge.  Appearance  of  fractures,  silky,  slightly  lamellar  ;  metal  well  drawn  down. 

j.  Fractured  Plate  B,  taking  zigzag  course  through  two  outside  rows  of  rivet  holes. 
Appearance  of  fractures,  silky  in  part,  granular  in  part ;  the  metal  in  the  silky  sections 
well  drawn  down,  the  granular  sections  not  much  reduced  in  thickness,  the  extremes 
of  thickness  after  fracture  being  .665"  in  the  silky  and  .840"  in  the  granular  metal. 
A  loud  report  accompanied  the  fracture  of  the  granular  metal. 

k.  Fractured  Plate  A,  taking  a  zigzag  course  through  two  outer  rows  of  rivet  holes. 
Appearance  of  fracture,  silky,  slightly  lamellar. 

/.  Fractured  Plate  B,  taking  a  zigzag  course  through  two  outside  rows  of  rivet 
holes.  Fracture  silky,  slightly  lamellar. 

m.  Fractured  Plate  A  along  outside  row  of  rivet  holes.  Fracture  silky,  slightly 
lamellar.  Mean  thickness  at  fracture,  .56  inch. 

«.  Fractured  Plate  A  along  outside  row  of  rivet  holes.   Fracture  silky,  slightly  lamellar. 

o.  Fractured  Plate  A  along  outside  row  of  rivet  holes.  Fracture  silky,  lamellar. 
One  seam  in  fractured  surface  $£ff  wide. 

p.  Fractured  Plate  A  along  outside  row  of  rivet  holes.     Fracture,  silky  lamellar. 

q.   Fracture  in  same  place  as  Hr     Appearance,  silky,  slightly  lamellar. 

r.  Fractured  Plate  B  along  outside  row  of  rivet  holes.  Appearance,  silky,  slightly 
lamellar.  Plates  open  at  butt  joint  ^  inch. 

s.  Fractured  Plate  B  along  outside  row  of  rivets,  beginning  the  fractures  at  edges 
and  extending  from  rivet  holes  toward  middle  of  plate.  Fracture  silky,  slightly 
lamellar  ;  metal  well  drawn  down. 

t.  Fractured  Plate  A  along  outside  row  of  rivets.  Appearance  of  fracture,  silky, 
slight  lamination. 

u.  Fractured  Plate  A  along  outside  row  of  rivets.  Appearance  of  fracture,  silky, 
slightly  lamellar  ;  metal  well  drawn  down. 

v.  Fractured  Plate  B ;  followed  outside  row  of  rivet  holes  in  part,  and  thence, 
through  inside  rows,  to  end  of  plate ;  sheared  two  end  rivets.  Fractures  silky, 
slightly  lamellar. 

w.  Fractured  Plate  A  along  outside  row  of  rivet  holes,  except  end  sections  and  one 
middle  section.  Appearance,  silky,  lamellar. 

x.  Sheared  every  rivet  in  the  joint  in  both  plates.  The  under  butt  strap  dropped 
to  the  floor.  Double  shear  in  Plate  A,  .three  rivets  ;  single  shear  in  Plate  B,  with  the 
exception  of  one  rivet,  which  sheared  in  two  planes. 


RIVETED   JOINTS. 


I99 


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200  MACHINE   DESIGN. 

TENSION  TESTS  OF  STRIPS  CUT  FROM  FRACTURED  ENDS  OF  RIVETED  JOINTS. 

These  strips  were  taken  from  the  middle  of  the  width  of  the  joint  plates  and  parallel 
to  the  direction  the  joints  were  pulled. 

Two  strips  were  taken  from  each  ;  one  was  annealed  by  heating  bright  red  and  cool- 
ing in  the  open  air  ;  the  duplicates  were  not  annealed  and  were  tested  as  taken  from  the 
fractured  joint. 

When  the  annealed  specimens  were  at  the  maximum  temperature,  centre-punch 
marks,  10"  apart,  were  stamped  on  one  edge,  and  about  the  time  the  color  had  left 
them  they  were  marked  again  on  the  other  edge.  After  cooling  to  70°  Fahr.  the  dis- 
tances between  these  marks  were  measured. 

The  amount  of  contraction,  therefore,  indicates  approximately  the  heat  at  which  the 
strips  were  annealed. 

48.     Riveting  Machines. 

Rivets  are  driven  either  by  a  succession  of  relatively  light  blows, 
as  in  hand-work  and  by  pneumatic  hammers,  or  by  heavy  and 
sustained  pressure,  as  in  hydraulic  machines.  In  the  latter  pro- 
cess, the  continuous  and  powerful  compression  of  the  hot  rivet- 
blank  upsets  the  shank,  fills  the  hole,  and  closes  the  plates,  while 
in  hammering,  especially  if  the  blows  are  light,  the  head  may  be 
formed  before  the  shank  is  upset  fully,  the  rivet  may  be  more  or 
less  loose  in  its  hole,  and  the  impact  tends  to  crystallize  the  metal. 
Owing,  however,  to  the  extremely  rapid  action  of  the  pneumatic 
hammer,  excellent  results  in  hull  and  structural  work  have  been 
obtained  by  its  use.  When,  as  in  marine  cylindrical  boilers,  the 
plates  are  thick  and  the  rivets  large,  hydraulic  riveting  is  necessary 
in  order  to  secure  tight  joints. 

Riveting  machines  may  be  "  fixed  "  and  powerful,  as  for  steam 
boilers  and  shop-riveting  in  general,  or  light  and  portable,  as  in 
the  types  used  for  hull  work  and  field-rivets.  The  essential  parts 
of  any  machine  are  a  stationary  "stake"  holding  the  die  which 
engages  the  rivet-head  and  a  piston  or  ram  driving  a  second  die 
which  upsets  the  shank  and  forms  the  point.  The  stake  or  its 
equivalent  forms  part  of  the  framing  of  the  machine.  In  the  pneu- 
matic hammer,  it  is  replaced  by  an  air-pressure  mechanism  known 
as  the  "pneumatic  holder-on."  In  portable  riveters,  the  riveting 
plunger  may  be  direct-acting  or  be  operated  through  linkage  from 
the  piston  rod.  An  auxiliary  cylinder,  actuating  a  plate-closing 
device,  has  been  used  for  clamping  the  joint  before  the  rivet  is  upset. 

Either  steam,  hydraulic,  or  pneumatic  power  is  used  in  riveting 
machines.  All  are  applied  to  drive  by  pressure  and  the  latter,  in 
the  pneumatic  hammer,  by  impact  as  well.  Steam  has  the  ad- 
vantages of  familiar  mechanism  and  the  absence  of  an  accumulator 


RIVETED   JOINTS. 


201 


or  compressor-plant ;  but  its  relatively  low  pressure  makes  large 
cylinders  necessary,  and,  owing  to  its  condensation,  expansibility, 
and  the  leakage  inevitable  with  piston-valves,  the  pressure  de- 
veloped is  not  uniform  and  is  delivered  largely  in  the  form  of  a 
blow  which  tends  to  crystallize  the  rivet.  These  objections,  ex- 
cept with  regard  to  condensation,  apply  in  the  main  to  pneumatic 
machines,  although  their  portability  gives  them  a  wide  field.  In 
hydraulic  riveting,  a  pressure  of  1,500  Ibs.  per  sq.  in.  is  used. 
This  gives  a  small  cylinder  requiring,  relatively,  but  little  fluid, 
while  the  practically  incompressible  and  inexpansible  character  of 
the  latter  makes  the  driving  stroke  a  powerful  and  uniform 
squeezing  of  the  metal  which  fills  the  hole  and  forms  the  point 
without  impact.  The  high  pressure,  however,  necessitates  strong 
and  accurately  made  joints,  and,  with  careless  handling  in  winter 
weather,  waste  water  in  cylinders  or  pipes  may  freeze.  Since 


FIG.  83. 


2O2 


MACHINE   DESIGN. 


the  fluid  in  the  driving  line  is  under  1,500  Ibs.  pressure,  its 
liability  to  freezing  is  slight.  A  mixture  of  one  third  crude 
glycerine  and  two  thirds  water  is  used  with  success  in  Canada 
and  northern  Russia. 

Riveting  machines,  in  their  power,  form,  and  fixed  or  portable 
character,  present  a  wide  variety  of  types.  The  descriptions  given 
below  refer  to  the  two  which  may  be  considered  as  the  extremes 
of  this  range. 

i.  HYDRAULIC  FIXED  RIVETER.  —  Fig.  83  shows  in  elevation 
the  riveter  of  this  type  built  by  Messrs.  R.  D.  Wood  and  Company. 

It  is  of  "triple  power,"  i.  e.,  it  exerts  any  one  of  three  pressures  upon  the  rivet, 
thus  fitting  it  not  only  for  work  of  the  heaviest  character,  but  also  for  that  upon  light 
plates  which  would  be  crushed  by  the  pressures  required  for  rivets  of  large  diameter. 
The  powers  and  sizes  of  the  standard  machines  of  this  type  are  : 

No.  i—  50,    35  or  15  tons  power  5',  6',  7',  8',      9/6",  IO'D"  and  12'  gaps. 

"    2—  60,    40  "  20     "       "      5',  6',  T,  8',      9'6",  io'6"    "  12'  " 

"    3—  75,    5o  "  25     "       "           T,  8',  io'6",            12'        "  17'  " 

"    4—100,    67  "  33     "       "                 8',  io'6",            12'        "  17'  " 

"    5 — 150,  100  "  50     "       "            8',  9/6//,  io'6",            i2/        "  17'  " 

«    6— 180,  120  "  60     "       "            8',  9'6",  lo'W,            12'        "  \T  " 
Usual  working  pressure,  1,500  pounds  per  square  inch. 

The  frame  is  a  single  casting  to  which  the  cylinder  is  bolted,  the  joint  being  tongued 
and  grooved  to  ensure  absolute  rigidity.  The  cylinder,  glands,  rams,  the  framing,  and 
hence  the  stakes,  are  made  from  open-hearth  steel  castings,  having  an  ultimate  tensile 
strength  of  70,000  Ibs.  per  sq.  in.,  an  elastic  limit  of  40,000  Ibs.  per  sq.  in.,  and  an 
elongation  of  20  per  cent,  in  an  8-in.  test-piece. 


FIG.  84. 

Fig.  84  gives  a  vertical  section  through  a  riveting  head,  with  rams  having  inside 
packing  of  leather.  The  section  in  Fig.  85  is  similar,  excepting  that  the  n>ms  are 
packed  outside  with  flax.  In  the  latter  arrangement,  the  packing  in  the  three  stuffing 
boxes  is  held  in  place  by  outside  glands  and  is,  hence,  accessible  readily  for  repacking 
or  adjustment. 


RIVETED   JOINTS. 


203 


ca 


FIG.  85. 


The  operation  of  the  ram  is  the  same  in  each  case.  Referring  to  Fig.  85,  it  will  be 
seen  that  there  are  tandem  cylinders,  A  and  B,  in  which  the  duplex  ram,  CD,  carrying 
the  riveting  head,  E,  reciprocates.  In  the  additional  cylinder,  F,  the  "pull-back 
ram,"  G,  moves.  The  riveter  is  fitted  with  a  distributing  valve  and  an  operating  valve. 
The  former  is  practically  a  double-stop  valve  and  may  be  adjusted  in  any  one  of  three 
positions,  viz. :  With  the  water  passage  to  the  small  cylinder,  A,  open  and  that  to  the 
large  cylinder,  B,  closed  ;  with  the  passage  open  to  B  and  closed  to  A  ;  with  the  pas- 
sages open  to  both  cylinders.  The  ram-areas  upon  which  the  accumulator-pressure  acts 
are  :  With  the  first  adjustment,  that  of  cylinder,  A  ;  with  the  second,  that  of  the  dif- 
ference in  area  between  cylinders  B  and  A  ;  and,  with  the  third,  the  full  area  of  cylin- 
der, B.  The  operating  valve  is  of  the  balanced  piston  type  with  leather  packing.  The 
accumulator-pressure  is  led  directly  to  the  pull-back  ram  without  passing  through  either 
of  the  valves  as  above.  This  ram  is,  hence,  always  in  action  and  its  back  pressure  must 
be  overcome  by  that  in  the  driving  cylinders  before  the  ram,  CD,  can  advance.  In 
riveting,  the  operator  first  sets  the  distributing  valve  for  the  pressure  desired ;  then 
moves  the  plates  until  the  rivet  is  opposite  the  dies  and  throws  the  operating  lever. 
Until  the  latter  is  withdrawn  to  its  original  position,  the  pressure  remains  upon  the 
rivet.  Since  the  operation  of  the  type  shown  in  Fig.  84  is  the  same  as  that  just 
described,  the  reference-letters  for  similar  parts  in  both  are  identical. 


FIG.   86. 


2.  PNEUMATIC  RIVETING  HAMMER.  —  Fig.  86  *  gives  a  longi- 
tudinal section  of  the  Boyer  "  Long-Stroke  Pneumatic  Hammer." 

Compressed  air  is  admitted  to  the  hammer  through  a  hose  coupled  at  the  lower  ex- 
tremity of  the  handle.     The  admission  is  controlled  by  a  main  throttle  valve  of  the 
American  Machinist,  April  25,  1901. 


204  MACHINE   DESIGN. 

balanced  piston  type.  This  valve  is  closed  by  a  spring  and  is  depressed  and  opened 
by  the  throttle-lever,  /,  which  is  pressed  by  the  thumb  of  the  operator.  The  riveting 
die,  a,  is  held  in  position  by  the  light  clip,  b,  only.  Hence,  if  it  is  not  pressed  against 
the  rivet,  the  first  blow  of  the  hammer,  r,  would  discharge  it  like  a  bullet.  To  prevent 
this,  an  auxiliary  spring-pressed  throttle  or  stop- valve,  c,  is  fitted,  which  valve  is  oper- 
ated by  two  rods,  as  d,  which  extend  through  the  body  of  the  hammer  and  have  their 
outer  ends  resting  upon  the  ring  e,  against  which  the  die-shank  abuts.  When,  there- 
fore, the  die  is  not  forced  firmly  against  a  rivet  —  although  the  main  throttle- valve  may 
be  open  —  the  auxiliary  valve  c  will  be  seated  by  air  and  spring  pressure  and  the  rods 
d,  ring  e,  and  die  a,  will  be  moved  slightly  to  the  right.  Since  both  valves  must  be 
open  before  the  piston,  r,  will  act,  the  auxiliary  valve,  c,  forms  a  safeguard. 

The  valves  which  control  the  air  in  its  pasage  to  and  from  the  ends  of  the  cylinder 
are  shown  at/and^.  They  are  hollow  and  of  short  stroke.  Rods,  as  h,  similar  to 
d,  lie  between  the  valves  in  the  walls  of  the  cylinder.  As  one  valve  moves  toward 
the  centre  of  the  cylinder  to  admit  air  at  its  end,  it,  through  the  rods,  pushes  the  other 
valve  away  from  the  centre,  so  that  the  exhaust  is  open  at  that  end. 

In  the  position  shown,  the  air  enters  the  inner  end  of  the  cylinder,  as  indicated  by 
the  arrow  i,  and  drives  the  piston,  r,  outward,  the  exhaust  escaping  as  shown  at  j. 
When  the  outer  end  of  the  piston  enters  the  valve,  g,  it  compresses  the  air  before  it, 
forming  a  cushion  which,  acting  upon  the  annular  end  of  g,  pushes  the  latter  to  the  left 
and  hence  valve  /also  through  the  rods,  h.  In  this  position,  the  ports  which  were 
open  previously  are  closed,  port  k  is  open  to  live  air,  and  exhaust  occurs  through  port 
/.  The  holes  in  which  the  rods,  d,  lie,  serve  also  as  passages  for  air  to  the  port  k.  On 
the  completion  of  the  return  stroke,  the  piston  enters  the  inner  valve,  _/)  and  the  valves  are 
driven  to  the  right. 


FIG.  87. 


This  hammer  weighs  about  17  Ibs.  and  is  made  for  driving 
rivets  from  I  in.  to  \\  in.,  diameter.  It  is  stated  that  it  requires 
20  cubic  feet  of  free  air  per  minute.  The  air-pressure  which  de- 
termines the  force  of  the  blow,  ranges  from  90  to  100  Ibs.  per 
sq.  in.,  The  hammer  may  be  used  without  a  supporting  frame. 


RIVETED   JOINTS.  205 

Its  operation,  with  such  frame  and  with  the  pneumatic  holder-on, 
is  illustrated  by  Fig.  87. 

49.     Riveted  Joints,  Marine  Boilers. 

Marine  cylindrical  boilers  are  of  the  internally  fired  type.  Fig. 
88  shows  one  half  of  a  longitudinal  and  one  half  of  a  transverse 
section  of  the  double-ended  boilers  of  the  U.  S.  Battleship  Kear- 
sargc.  The  diameter  is  15  ft.,  8  in.;  the  length,  21  ft.  As 


FIG. 


shown,  the  shell,  A,  is  made  of  three  courses  of  four  plates  each ; 
the  front  and  back  heads,  B,  are  each  built  up  of  three  plates,  the 
upper  of  which  is  curved  backward  to  meet  the  shell  ;  the  furnaces 
are  cylindrical  and  are  corrugated  to  give  strength  ;  the  combus- 
tion chamber,  C  (one  to  each  pair  of  furnaces  and  two  to  each 
end),  is  built  of  flat  plates  throughout,  except  at  the  outer  side 
which  is  curved  so  that  it  is  concentric  with  the  shell.  The  boiler 
is  braced  by  stays,  JD,  in  the  steam  and  water  spaces,  girders,  E, 
upon  the  tops  of  the  combustion  chambers,  screw-stays  at  the  sides 
and  backs  of  the  latter,  and  by  stay -tubes. 


206 


MACHINE    DESIGN. 


The  longitudinal  seams  of  the  shell  are  double-strapped  butt- 
joints,  treble-riveted ;  the  circumferential  seams  (central)  are  lap- 
joints,  treble-riveted  ;  the  joints  of  heads  with  shell  are  lapped  and 
double-riveted,  except  with  the  curved  plates  which  are  treble- 
riveted  ;  the  head  plates  are  united  by  lapped  seams  —  the  upper, 
quadruple,  the  lower,  double-riveted ;  all  joints  in  furnaces  and 
combustion  chambers  are  single-riveted  lap  seams. 

i.  RIVET  AND  PLATE  METALS. — The  physical  and  chemical 
characteristics  of  rivet-metals,  as  prescribed  in  the  specifications 
(1901)  of  the  Bureau  of  Steam  Engineering,  U.  S.  Navy,  have 
been  given  in  §  32.  The  tests  for  rivets,  as  laid  down  in  these 
specifications,  are : 

Rivets.  —  Samples  from  each  lot  are  to  stand  the  following  tests  without  fracture, 
test  (a)  being  applied  to  one  lot,  and  (6)  to  a  second,  etc.  : 

(a)  Bend  double  cold  to  a  curve  of  which  the  inner  diameter  is  equal  to  the  diameter 
of  the  rivet. 

(3)  Bend  double  hot  through  an  angle  of  180°  flat  back. 

(c)  The  head  to  be  flattened  when  hot  without  cracking  at  the  edges  until  its 
diameter  is  two  and  one  half  times  the  diameter  of  the  shank. 

(a )  The  shanks  of  sample  rivets  to  be  nicked  on  one  side  and  bent  cold  to  show  the 
quality  of  the  material. 

Surface  Inspection.  —  Rivets  shall  be  true  to  form,  concentric,  and  free  from  in- 
jurious scale,  fins,  seams,  and  all  other  injurious  defects.  If  the  material  is  found  to  be 
very  uniform  and  none  of  the  tests  made  of  a  series  of  lots  fail,  the  inspector  may  discon- 
tinue the  tests  after  he  has  made  enough  to  satisfy  himself  that  the  whole  of  the  material 
on  the  order  is  satisfactory. 

Note.  —  In  measuring  the  diameter  of  rivets  the  inspector  will  allow  for  the  trade 
custom  of  making  rivets  with  an  actual  diameter  slightly  (about  y1^  of  an  inch)  less  than 
the  nominal  diameter. 


Class. 

Material. 

Mini- 
mum 
Tensile 
Strength. 

Mini- 
mum 
Elastic 
Limit. 

Elon- 
gation. 

Maximum 
Amount  of. 

Cold  Bend  about  an 
Inner  Diameter. 

P. 

S. 

Class   A. 

Class   B. 
Class  C.» 

Open-hearth 
steel. 

Open-hearth 
steel. 
Open-hearth 
or  Besse- 
mer. 

Lbs.  per 
sg.  in. 
70,000 

6o,OOO 

To  be  ir 

the   / 
Struct 

Lbs.  per. 
sq.  in. 

37,000 

32,000 

accorda 
Lssociatioi 
ural  Steel 

Per  ct.  in 

8  inches. 
22 

25 

ace  with 
i   of    Am 
,"  revisec 

.04 

.04 

the   « 
erican 
ljuly 

.03 

•03 

Stanc 
Stee 
1896 

Equal     to     thick- 
ness of  plate  and 
through  I  80°. 
Flat  back  through 
1  80°. 
ard  Specifications  of 
Manufacturers   for 

*  Class  C  plates,  shapes,  etc.,  will  be  inspected  at  the  building  yard  and  not  at  the 
place  of  manufacture  except  upon  special  request  of  the  contractor.  No  physical  or 
chemical  test  will  be  made  unless  from  the  appearance  of  the  plates  giving  evidence  of 
overheating,  cold-rolling,  etc.,  or  for  other  reasons,  the  inspector  has  doubts  as  to  their 
fitness  for  the  purpose  for  which  they  are  intended. 


RIVETED   JOINTS. 


207 


The  physical  and  chemical  characteristics  of  steel  boiler-plate, 
as  similarly  prescribed,  are  : 

1.  The  physical  and  chemical    characteristics  of  steel  boiler-plate   are   to   be   in 
accordance  with  the  table  on  page  206. 

2.  Kind  of  Material.  —  Steel  for  boiler-plates  of  all  grades  (except  Class  C)  shall 
be  made  by  the  open-hearth  process,  and  shall  contain  not  more  than  four  one-hun- 
dredths  of  I  per  cent,  of  phosphorus,  and  not  more  than  three  one-hundredths  of  I  per 
cent,  of  sulphur. 

2.  PROPORTIONS  OF  RIVETS.  —  The  standard  boiler  rivet  for  the 
U.  S.  Navy  is  of  the  "pan-head,"  or  conical  frustum,  type.  The 
head  and  point  are  alike.  Table  X  LI  I.  gives  the  proportions.  In 
this  table,  a  is  the  diameter  of  the  rivet,  b  the  greatest  and  d  the 
least  diameter  of  the  head,  and  c  is  the  height  of  the  latter.  The 
angle  of  the  sides  is  about  65°  in  the  i-in.  rivet,  a  and  d  are 
equal. 

TABLE  XLII. 
(BOILER  RIVETS,  U.  S.  NAVY.) 


a 

3 

c 

^ 

Wt.   of 
lo-Heads. 

r 

jl" 

1" 

f 

.331  Ibs. 

•531 
•713 

i 

| 

A 

f 

1.007 

il 

J 

f 

$ 

1-373 

| 

A 

1 

f 

I-55I 

it 

A 

ii 

i.t 

2.032 

^ 

A 

ii 

^. 

2.258 

it 
i 

| 

if 

ilf 

2.871 
3.584 

i_i 

it 

it 

iA 

3-91 

i  £ 

-        it 

ii 

4.761 

t, 

i 

iA 

5-17 

i 

if 

i? 

6.215 

£A 

i 

i 

TA 

7-391 

The  rivet-heads  used  for  boilers  at  the  Union  Iron  Works  are 
"  button -head  "  or  spherical.  The  proportions  are  : 

Diameter  of  shank  =  d ; 

head  =  f</+Ty; 
Depth  "     =\d. 

3.  PROPORTIONS  OF  JOINTS.  —  The  following  tables  give  the 
proportions  of  the  principal  seams  of  typical  cylindrical  boilers 
of  the  U.  S.  Navy.  The  plates  and  rivets  are  of  steel,  d  is  the 
diameter  of  the  rivet-hole,  /  is  the  greatest  pitch,  V  is  the 


208 


MACHINE   DESIGN. 


distance  between  the  rivet- rows  in  staggered  riveting,  and  P\  the 
similar  distance  between  the  outer  and  the  next  row,  when  alter- 
nate rivets  in  the  outer  row  are  omitted.  The  general  dimensions 
and  thickness  of  sheets  are  : 


t 

% 

I 
a 

3 

!! 

180 
180 
180 

Diameter. 

II 

i 
1 

Thickness  of  Sheets. 

I 

Head. 

fa 

!«' 

H£ 

P 

Butt  Straps. 

1 

2 
S 

| 

§ 

i 

15'  8" 
10  6 

7   9t 

20'    10" 

10  6 
9   9t 

"A 

I 
if 

1 

| 

I 

1 

| 

1 

t 

1 

The  proportions  of  the  joints  are  : 


ll 

Seam. 

Kind  of  Joint. 

d 

/ 

V 

^ 

* 

I 

Shell,  longitudinal. 

Double  strapped,  butt,  triple  riveted, 
zigzag,  alternate  rivets,  outer  row, 

If 

8& 

2f 

sA 

. 

omitted. 

Double  strapped,  butt,  triple  riveted, 

2 

<«                « 

zigzag,  alternate  rivets,  outer  row, 

I& 

7 

If 

2ii      iJL 

omitted. 

Double  strapped,  butt,  triple  riveted, 

3 

«                « 

zigzag,  alternate  rivets,  outer  row, 

1 

54 

I  1 

2  i 

I  1 

omitted. 

i 

Shell,  circumferential. 

Lap,  triple  riveted,  zigzag. 

i  i  1  4A 

2  3 

2  \ 

2 

"                " 

Lap,  double  riveted,  zigzag. 

if 

3t 

2 

2A 

3 

a                tt 

tt         tt             tt          tt 

I_3 

I 

I—  w- 

I 

Head  to  shell. 

tt         tt             if          tt 

iX 

4? 

2 

I  | 

2 

"            " 

"         "             "          " 

i  \ 

3A 

I 

l}£ 

3 

tt           n 

tt         tt             tt          tt 

IT^T 

I 

I  i 

i 

Front  head,  upper. 

Lap,  quadruple  riveted,  zigzag. 
V,  lower  row  =  2iV 

I& 

5 

2f 

II 

Lap,  triple  riveted,  zigzag  ;    alter- 

2 

tt             n 

nate  rivets,  middle   row  omitted  ; 

IrV 

3l 

If 

pitch,  outer  rows,  3^,  inner,  7^. 

3 

i 
i 

Front  head,  lower. 
Furnace  to  tube  sheet. 

Lap,  triple  riveted,  zigzag. 
Lap,  double  riveted,  zigzag. 
Lap,  single  riveted. 

i 

3i 
3j 

:A 

ii 

2 

ft                         ct 

"         "           " 

2 

a 

3 

if                      tt 

tt         tt          tt 

2  ^ 

1  1 

Tube-sheet  to  combus- 

* 

i 

tion  chamber  and  com- 

it        a          tt 

15 

2i 

ITS 

bustion  chamber  seams. 

16 

4 

Tube-sheet  to  combus- 

2 

tion  chamber  and  com- 

tt        tt          tt 

I 

2  3 

i  i 

bustion  chamber  seams. 

TS 

4 

Tube-sheet  to  combus- 

3 

tion  chamber  and  com- 

it        tt           tt 

15 

2  -J- 

I   T 

bustion  chamber  seams. 

8 

5 

RIVETED    JOINTS. 


209 


4.  WEIGHT  OF  RIVETS.  —  The  total  weight  and  the  weight  of 
rivets  are  given  below  for  three  cylindrical  boilers  of  large  size  for 
the  U.  S.  Navy.  The  weight  given  is  that  of  the  boiler  simply 
without  fittings,  such  as  grate-bars,  valves,  lagging,  etc.  The 
plates  and  rivets  are  of  steel. 


Working  Pres- 
sure, Ibs. 

Diameter. 

Length. 

Total  Weight 
of  Boiler,  Ibs. 

Weight  of 
Rivets,  Ibs. 

Rivet-percen- 
tage of  Total 
Weight. 

160 
160 
135 

I5'o" 

I5'3" 

I4'8" 

1  8V 
21  '3" 
19/2" 

135,793 
149,634 
108,128 

5,788 

6,218 
5,39i 

4.26 
4.16 
4.98 

5.  THE  U.  S.  BOARD  OF  SUPERVISING  INSPECTORS  OF  STEAM 
VESSELS.  —  The  regulations  (Jan.,  1901)  of  this  board  give  the 
following  formulas  for  the  proportions  of  single-  and  double-rivetod 
lap-joints  for  both  iron  and  steel  boilers.  Let : 

p  =r  greatest  pitch  of  rivets,  ins.  ; 
n  =  number  of  rivets  in  one  pitch-section  ; 
pd  =  diagonal  pitch,  ins.  ; 
d=  diameter  of  rivets,  ins.  ; 
T-=.  thickness  of  plate,  ins.  ; 
F=  distance  between  rows  of  rivets,  ins.  ; 
E  =  distance  from  edge  of  plate  to  centre  of  rivet,  ins. 

For  iron  plates  and  iron  rivets  : 


+  d. 


For  steel  plates  and  steel  rivets  : 


For  all  joints  : 


For  double  ^/Jam-riveted  joints,  V  should  not  be  less  than  zd\  but  it  is  more  desirable 
that  V should  not  be  less  than—  -^ .     For  ordinary,  double,  az^za^-riveted  joints  : 


For  double,  zigzag-riveted  lap  joint,  iron  and  steel  : 

*±4* 

10 
For  single-riveted  lap  joints  : 

Maximum  pitch  =  (i.3iX  T)  +  l\- 
For  double-riveted  lap  joints  : 

Maximum  pitch  =  (2.62  X  T}  -j-  if. 


210  MACHINE   DESIGN. 

These  formulae  are  equivalent  to  those  of  the  British  Board  of 
Trade  and  are  similar  in  many  respects  to  those  given  in  Traill's 
handbook  (§  43).  From  the  latter,  tables  of  single-  and  double- 
riveted  lap  joints,  for  both  iron  and  steel,  are  quoted  in,  and 
authorized  for  use  by,  these  regulations. 

6.  PROCESS  OF  RIVETING.  —  U.  S.  Naval  specifications  for 
boilers  require  that  "  hydraulic  riveting  shall  be  used  wherever 
possible.  In  parts  where  hydraulic  riveting  cannot  be  used,  the 
rivet-holes  shall  be  coned  and  conical  rivets  used.  Seams  will  be 
calked  on  both  sides  in  an  approved  manner." 

50.     Riveted  Joints,  Locomotive  Boilers. 

The  following  data  refer  to  the  practice  of  the  Baldwin  Loco- 
motive Works. 

i .   RIVET  AND  PLATE  METALS.  —  The  specifications  are  : 

Boiler  and  Fire- Box  Steel.  —  All  plates  must  be  rolled  from  steel  manufactured 
by  the  open-hearth  process,  and  must  conform  to  the  following  chemical  analysis  : 


BOILER  STEEL. 

FURNACE  STEEL. 

Carbon,  between 

o.  15  and  0.25  per  cent. 

1.  15  and  0.25  per  cent 

Phosphorus,  not  over 

0.05  per  cent. 

0.03  per  cent. 

Manganese,          " 

0.45       « 

0-45       " 

Silicon, 

0.03       " 

0.03       " 

Sulphur,               " 

0.05       " 

0.035     " 

No  sheets  will  be  accepted  that  show  mechanical  defects.  A  test  strip  taken  length- 
wise from  each  sheet  rolled  and  without  annealing  should  have  a  tensile  strength  of 
60,000  pounds  per  square  inch,  and  an  elongation  of  25  per  cent,  in  section  originally 
8  inches  long.  Sheets  will  not  be  accepted  if  the  test  shows  a  tensile  strength  of  less 
than  55)000  pounds,  or  greater  than  65,000  pounds  per  square  inch,  nor  if  the  elonga- 
tion falls  below  20  per  cent. 

Fire-Box  Copper. — Copper  plates  for  fire-boxes  must  be  rolled  from  best  quality 
Lake  Superior  ingots  ;  they  must  have  a  tensile  strength  of  not  less  than  30,000  pounds 
per  square  inch,  and  an  elongation  of  at  least  20  per  cent,  in  section  originally  2  inches 
long. 

Stay-Bolt  Iron.  —  Iron  for  stay-bolts  must  be  double-refined,  and  show  an  ultimate 
tensile  strength  of  at  least  48,000  pounds  per  square  inch,  with  a  minimum  elongation 
of  25  per  cent,  in  a  test  section  8  inches  long.  Pieces  24  inches  long  must  stand  bend- 
ing double,  both  ways,  without  showing  fracture  or  flaw.  Iron  must  be  rolled  true  to 
gauges  furnished,  and  permit  of  cutting  a  clean,  sharp  thread. 

Copper  Stay- Bolts.  —  Copper  stay-bolts  must  be  manufactured  from  the  best  Lake 
Superior  ingots  ;  they  must  have  an  ultimate  tensile  strength  of  not  less  than  30,000 
pounds  per  square  inch,  and  an  elongation  of  at  least  20  per  cent,  in  section  originally 
2  inches  long. 

The  general  practice  of  this  company  is  to  use  iron  rivets  of 
the  quality  required  as  above  for  stay-bolts. 


RIVETED   JOINTS. 


211 


2.  PROCESS  OF  RIVETING.  —  All  parts  of  the  boiler  which  can 
be  reached  by  fixed  or  portable  machines  are  riveted  by  hydraulic 
pressure.     The  latter  for  iron  or  steel  rivets  is  : 

i^  in.  diameter,  100  tons. 

'i  "  75     " 

i  "  66     " 

I  «  50     •« 

!  "  33     " 

f  "  25     « 

For  copper  rivets,  a  pressure  ranging  from  25  to  33  tons  —  never 
exceeding  the  latter  —  is  used.  The  driving  head  of  the  rivet  is 
made  the  same  in  height  as  the  diameter  of  the  shank. 

3.  PROPORTIONS  OF  JOINTS.  —  Tables  XLIII.,  XLIV.,  XLV., 
XLVI.  give  the  size  and  arrangement  of  rivets  for  various  thick- 
nesses of  sheets  in  single-  and  double-riveted  lap  seams  and  quad- 
ruple- and  sextuple-riveted  butt  joints,  with  double  straps  unequal 
in  width. 

TABLE    XLIII. 

SlNGLE-RlVETED   LONGITUDINAL  SEAMS.      ( FOR  ALL  PRESSURES.)     FOR  OUTSIDE 

FIRE-BOX  SEAMS  OF  RADIAL  STAY  BOILERS. 

(BALDWIN  LOCOMOTIVE  WORKS.  ) 


PL 

ite. 

^ 

£ 

J 

Thickness. 

Material. 

if 

Iron. 

1" 

\" 

2- 

-" 

Steel. 

| 

I 

2} 

• 

Iron. 

| 

2 

Steel. 

3 

2 

Iron. 

| 

2 

Steel. 

| 

2 

Iron. 

5 

i 

2 

Steel. 

5 

i 

2 

Iron. 

1 

i 

I] 

• 

Steel. 

i 

2, 

'-            " 

i 

3 

" 

i 

3 

« 

i 

3 

ft 

" 

i\ 

. 

3 

i 

212 


MACHINE   DESIGN. 


TABLE   XLIV. 

DOUBLE-RIVETED  SEAMS. 
(BALDWIN  LOCOMOTIVE  WORKS.) 


fit 

te. 

B 

d 

£> 

.£ 

Per  cent, 
of  solid 

Thickness. 

Material. 

plate. 

3// 

Steel. 

!// 

2// 

// 

I  // 

^ 

^ 

62 

TV 

2J 

A 

4- 

65 

I 

24 

A 

4i 

65 

rV 

I 

2f 

\ 

4^ 

63 

I 

I 

2| 

i 

41 

63 

U 

H 

3 

iU 

9i 

62 

i 

4 

3i 

2 

if 

5i 

64 

TABLE  XLV. 

QUADRUPLE  BUTT-JOINT  SEAMS  WITH  WELDED  ENDS. 
(BALDWIN  LOCOMOTIVE  WORKS.) 


Plate. 

A 

B 

C 

z> 

^ 

F 

C 

H 

/ 

^ 

Thickness. 

Material. 

r 

Steel. 

r 

2// 

2^ 
2I 

2^ 

i/x 

ft 

f 

r 

8 

s 
3 

r 

t 

r 

81.2 
82.5 
82.5 

o 

I 

2| 

3 

6 

9       12 

A 

si.8 

4 

I 

2^- 

3 

6 

9      12 

if 

JLf 

81.8 

| 

H 

i 

1 

3i 
3i 
3i 

6* 
7 

7 

w| 

13 
14 

14 

f 

1 

81.2 
80.7 

80.7 

RIVETED   JOINTS. 

TABLE  XLVI. 

SEXTUPLE  BUTT- JOINT  SEAMS  WITH  WELDED  ENDS. 
(BALDWIN  LOCOMOTIVE  WORKS.) 


2I3 


Thickness.     Material. 


Steel. 


87 

86.5 
85.7 
85.7 
85.0 
84.0 
84.0 
85.0 


4.   LOCATION  OF  JOINTS.  —  Fig.  89  gives  a  longitudinal  section, 
omitting  tubes  and  braces,  of  a  Radial  Stay,  Wagon-top,  locomo- 


214 


MACHINE    DESIGN. 


tive  boiler,  as  built  by  this  company.  In  Fig.  90  there  is  shown 
a  transverse  semi-section  through  the  fire-box.  The  barrel  is  built 
of  three  courses  of  one  sheet  each, 
the  thicknesses,  beginning  at  the 
furnace  tube-sheet,  being  ^  in.,  ^ 
in.,  and  i|  in.,  respectively.  The 
remaining  shell  sheet  is  ^  in.  thick. 
The  thicknesses  of  the  tube-sheets, 
crown-sheet,  and  fire-box  front  and 
side-sheets  are,  respectively,  y2  in., 
T/%  in.,  and  ^  in.  The  longitudinal 
and  circumferential  seams  of  the 
barrel  are,  respectively,  quadruple- 
riveted  butt  (unequal  straps)  and 
double-riveted  lap  joints  ;  the  re- 
maining seams  are  single-riveted  lap 
joints.  Since  rivet-heads  in  the  fur- 
nace are  liable  to  be  burned  off,  the 
rivets  are  counter-sunk  in  fire-box 
and  side  sheets  for  36  ins.  from  the 
bottom  upward.  The  proportions 
of  the  principal  seams  are  given  in 
the  following  list,  the  notation  being 
that  of  the  joint-tables  previously 
given  and  the  locations  being  num- 
FIG.  90.  bered  in  Figs.  89  and  90. 


Seam. 

Plate. 

No. 

Kind. 

Thick. 

I 

Quadruple,  butt. 

ir 

ft 

3" 

31// 

if 

6*" 

13" 

H" 

I// 

2 

| 

3i 

3? 

1  1 

7 

14 

^ 

^ 

5. 

Vr 

3? 

1  1 

7 

14 

3 

1 

•4 

Double-riveted  lap. 

ti>     1 

3 

'U 

Si 

i 

i                « 

if 

2 

Tf 

:f 

sl 

4f 

7 

Single-riveted  lap. 

i>  H 

2 

4 

9 

Iu 

II 

;         « 

& 

! 

• 
• 

2 
2 
2 

K>  »v>  K>  O> 

*Hi-*)-'H« 

RIVETED   JOINTS.  21$ 

51.     Riveted  Joints,  Stationary  Boilers. 

Cylindrical  boilers  for  stationary  service  are  usually  of  the  ex- 
ternally fired  type,  the  shell  containing  only  the  bracing  and  the 
tubes  or  flues. 

1.  AMERICAN    BOILER    MANUFACTURERS'    ASSOCIATION. — The 
following  extracts  from  the  Uniform  American  Boiler  Specifications 
adopted  in  October,  1898,  by  this  association  are  given  through 
the  courtesy  of  E.  D.  Meier,  Esq.,  chairman  of  the  committee 
which  formulated  these  specifications. 

2.  Steel.  —  Homogeneous   steel    made  by  the  open  hearth  or  crucible   processes, 
and  having  the  following  qualities,  is  to  be  used  in  all  boilers  : 

Tensile  Strength,  Elongation,  Chemical  Tests.  —  Shell  plates  not  exposed  to  the 
direct  heat  of  the  fire  or  gases  of  combustion,  as  in  the  external  shells  of  internally  fired 
boilers,  may  have  from  65,000  to  70,000  pounds  tensile  strength  ;  elongation  not  less 
than  24  per  cent,  in  8  inches ;  phosphorus  not  over  .035  per  cent.  ;  sulphur  not  over 
.035  per  cent. 

Shell  plates  in  any  way  exposed  to  the  direct  heat  of  the  fire  or  the  gases  of  combus- 
tion, as  in  the  external  shells  or  heads  of  externally  fired  boilers,  or  plates  on  which  any 
flanging  is  to  be  done,  to  have  from  60,000  to  65,000  pounds  tensile  strength  ;  elonga- 
tion not  less  than  27  per  cent,  in  8  inches  ;  phosphorus  not  over  .03  per  cent.  ;  sulphur 
not  over  .025  per  cent. 

Fire-box  plates  or  such  as  are  exposed  to  the  direct  heat  of  the  fire,  or  flanged  on  the 
greater  portion  of  their  periphery,  to  have  55,000  to  62,000  pounds  tensile  strength ; 
elongation  30  per  cent,  in  8  inches  ;  phosphorus  not  over  .03  per  cent.  ;  sulphur  not 
over  .025  per  cent. 

For  all  plates  the  elastic  limit  to  be  at  least  one  half  the  ultimate  strength  ;  per- 
centage of  manganese  and  carbon  left  to  the  judgment  of  the  steel  maker.  *  *  * 

3.  Rivets  to  be  of  good  charcoal  iron,  or  of  a  soft,  mild  steel,  having  the  same 
physical  and  chemical  properties  as  the  fire-box  plates,  and  must  test  hot  and  cold  by 
driving  down  on  an  anvil  with  the  head  in  a  die  ;  hy  nicking  and  bending,  by  bending 
back  on  themselves  cold,  without  developing  cracks  or  flaws.  *  *  * 

10.  Riveting. — Holes  made  perfectly  true  and  fair  by  clean-cutting  punches  or 
drills.  Sharp  edges  and  burrs  removed  by  slight  countersinking  and  burr  reaming 
before  and  after  sheets  are  joined  together. 

Under  side  of  original  rivet  head  must  be  flat,  square  and  smooth.  For  rivets  ^  inch 
to  \\  inch  diameter  allow  i  ^  diameters  for  length  of  stock  to  form  the  head,  and  less  for 
larger  rivets.  Allow  5  per  cent,  more  stock  for  driven  head  for  button  set  or  snap 
rivets.  Use  light  regulation  riveting  hammers  until  rivet  is  well  upset  in  the  hole ; 
after  that  snap  and  heavy  mauls.  For  machine  riveting  more  stock  to  be  left  for  driven 
head  to  make  it  equal  to  original  head,  as  fixed  by  experiment. 

Total  pressure  on  the  die  about  80  tons  for  i^-inch  to  i^-inch  rivets  ;  65  tons  for 
i -inch  ;  57  tons  for  ||-inch  ;  35  tons  for  ^f-inch  rivets. 

Make  heads  of  rivets  equal  in  strength  to  shanks  by  making  head  at  periphery  of 
shank  of  a  height  equal  to  y£  diameter  of  shank  and  giving  a  slight  fillet  at  this  point. 

Approximately,  make  rivet  holes  double  thickness  of  thinnest  plate  ;  pitch  three  times 
rivet  hole  ;  pitch  lines  of  staggered  rows  %  pitch  apart ;  lap  for  single-riveting  equal  to 
pitch,  for  double-riveting  i^  pitch,  and  %  pitch  more  for  each  additional  row  of 


216 


MACHINE    DESIGN. 


rivets ;  exact  dimensions  determined  by  making  resistance  to  shear  of  aggregate  rivet 
section  at  least  10  per  cent,  greater  than  tensile  strength  of  net  or  standing  metal. 

11.  Rivet  Holes  punched  with  good  sharp  punches  and  well-fitting  dies  in  A.  B.  M. 
A.  steel  up  to  $  inch  thickness  ;  in  thicker  plates  punch  and  ream  with  a  fluted  reamer, 
or  drill  the  holes. 

12.  Drift  Pin  to  be  used  only  with  light  hammers  to  pull  plates  into  place  and 
round  up  the  hole,  but  never  to  enlarge  or  gouge  holes  with  heavy  hammers.   *  *  * 

25.  Rivet  Seams  when  proportioned  as  prescribed  in  Section  10  with  materials  tested 
as  per  Sections  2  and  3  shall  have  4^  as  factor  of  safety  ;  when  not  so  tested,  but  in- 
spection of  materials  indicates  good  quality,  a  factor  of  safety  of  5  is  to  be  taken,  and  at 
most  55,000  Ibs.  tensile  strength  assumed  for  the  steel  plate  and  40,000  Ibs.  shear 
strength  for  the  rivets,  all  figured  on  the  actual  net  standing  metal. 

2.  THE  HARTFORD  STEAM  BOILER  INSPECTION  AND  INSURANCE 
Co.  —  The  following  data  refer  to  the  practice  of  this  company. 
The  specifications  for  horizontal  tubular  steam  boilers  require  that 
the  material  for  shell  plates  and  heads  shall  be  Open  Hearth  Fire- 
box Steel  and  best  Open  Hearth  Flange  Steel,  respectively ;  that 
the  longitudinal  and  girth  seams  shall  be,  respectively,  of  the  butt- 


FIG.  91. 

joint  type  with  double-covering  strips  and  the  single-riveted  lap- 
joint  type ;  and  that  the  rivet-holes  shall  be  drilled  in  place,  i.  e., 
holes  punched  at  least  \  in.  less  than  full  size,  then  courses  rolled 
up,  covering  plates  and  heads  bolted  to  courses  with  all  holes  to- 
gether perfectly  fair,  rivet-holes  drilled  to  full  size,  and  finally 
plates  taken  apart  and  burrs  removed.  No  rivets  shall  be  driven 
in  unfair  holes  ;  such  holes  must  be  brought  in  line  with  a  reamer 


RIVETED   JOINTS.  2 1/ 

Tables  XLVIL,  XLVIIL,  XLIX.,  L.  and  Figs.  91  and  92  give 
the  proportions  of  longitudinal  and  circumferential  or  girth  seams. 
The  inner  covering  strap  of  the  butt  joints  is  wider  than  the  outer. 


I .±c*I 


FIG.  92. 

The  inner  row  or  rows  of  rivets  have  half  the  pitch  of  the  outer 
row.  The  rivets  of  the  latter  pass  through  the  plate  and  inner 
covering  strap  only  and  are  thus  in  single  shear.  The  joints  are 
proportioned  for  steel  plates  and  iron  rivets.  The  tensile  strength 
of  plates  is  taken  as  60,000  Ibs.  per  sq.  in.  of  section  and  the 
shearing  resistance  of  rivets  (single  shear)  as  38,000  Ibs.  per  sq.  in. 
of  section.  The  diameter  of  rivet  holes  is  Jg  in.  greater  than  the 
diameter,  d,  of  the  rivets.  The  notation  of  the  tables  is  : 

C  =  circumferential  or  girth  seam  ; 
L  =  longitudinal  seam  ; 
T  =  thickness  of  plate,  ins.  ; 
/  =  thickness  of  outer  butt-strap,  ins. ; 
tl  =  thickness  of  inner  butt-strap,  ins. ; 
d  =  diameter  of  rivet,  ins.  ; 
p  =  greatest  pitch  of  rivets,  ins. ; 


218 


MACHINE   DESIGN. 


V=  distance  between  rivet-rows,  staggered  riveting,  ins.  ; 

Pj  =  distance  between  outer  and  next  row,  staggered  riveting, 
when  alternate  rivets  are  omitted  in  outer  row,  ins.  ; 

E  =  distance  from  centre  of  nearest  rivet  to  edge  of  plate  or 
strap,  ins.  ; 

A  =  total  width  of  outer  butt-strap,  ins. ; 

B  =  total  width  of  inner  butt-strap,  ins. 


TABLE  XLVII. 

CIRCUMFERENTIAL  SEAM,  C,  SINGLE-RIVETED  LAP  ;  LONGITUDINAL  SEAM,  Z, 
DOUBLE-  (STAGGERED)  RIVETED  LAP. 

(HARTFORD  STEAM  BOILER  INSP.  AND  INS.  Co.) 


Plate  Thickness. 

Seam. 

d 

P 

F 

^ 

I// 

C 

\\" 

2T8// 

i|/7 

^ 

L 

\\ 

2  \ 

IH// 

ij 

i 

C 

3 

2  | 

| 

L 
C 
L 
C 
L 

i 

2* 

1 

iH 

1 

i 

C 

i 

2  \ 

^ 

L 

i 

3fVff 

2tV 

Jtf 

TABLE  XLVIII. 

CIRCUMFERENTIAL  SEAM,  C,  SINGLE-RIVETED  LAP  ;  LONGITUDINAL  SEAM,  Z, 
TREBLE-  (STAGGERED)   RIVETED  LAP. 

(HARTFORD  STEAM  BOILER  INSP.  AND  INS.  Co.) 


Plate  Thickness. 

Seam. 

d 

p 

y 

JE 

r 

C 

5  // 

2h" 

j  ^ 

I 

L 

5 

3 

2// 

j  i 

1 

C 

L 
C 

f 

3 

2  - 

•A 

ii 

1 

L 

3 

3- 

2T% 

rV 

C 

1 

2 

jl.3 

T\ 

L 

I 

3 

2  I. 

ll| 

1 

C 
L 

» 

2 

3} 

\ 

M 

1! 

RIVETED   JOINTS. 


219 


TABLE  XLIX. 

DOUBLE-  (STAGGERED)  RIVETED  BUTT  JOINTS  WITH  UNEQUAL  STRAPS.     ALTER. 

NATE  RIVETS  OMITTED  IN  OUTER  Row. 
(HARTFORD  STEAM  BOILER  INSP.  AND  INS.  Co.) 


Efficiency. 


4 


9" 


83.0^ 
82.9 
82.0 
80.0 


TABLE  L. 

TREBLE-  (STAGGERED)  RIVETED  BUTT  JOINTS  WITH  UNEQUAL  STRAPS.     ALTER- 
NATE RIVETS  OMITTED  IN  OUTER  Row. 
(HARTFORD  STEAM   BOILER  INSP.  AND  INS.  Co.) 


tt 


14' 


Efficiency. 


87.5 

86.0 
86.6 


52.     Riveted  Joints,  Structural  Work. 

The  tables  and  other  data  given  in  this  section  refer  principally 
to  the  practice  of  the  American  Bridge  Company. 

i.  RIVET  AND  PLATE  METALS.  —  General  specifications  for 
structural  steel  have  been  given  in  §  37.  For  steel  railroad 
bridges  this  company  requires  : 

All  steel  to  be  made  by  Open  Hearth  process.  Per  cent,  of  phosphorus  :  Acid,  .08; 
basic,  .05. 


Grades. 

Rivet. 

Soft. 

Medium. 

Lit.  strength,  Ibs.  per  sq.  in. 
Elongation,  per  cent. 
Elastic  limit. 

48-58,000 
26 
\  ult.  str. 

52-62,000 

25 
\  ult.  str. 

60-70,000 
22 
\  ult.  str. 

For  rivet  and  soft  steel,  test-piece  to  bend  180°  flat  on  itself;  for  medium  steel,  180° 
to  a  diameter  equal  to  thickness  of  piece  —  in  all  cases  without  fracture  on  outside  of 
bent  portion.  • 

In  general  practice,  field-rivets,  i.  e.,  those  driven  in  course  of 
erection,  are  frequently  of  wrought  iron,  since  its  range  of  riveting 
temperature  is  less  affected  than  that  of  steel  by  cooling  and  delay. 

2.  RIVET  PROPORTIONS.  —  The  diameter  ranges  between  |  in. 
and  i  in.,  the  usual  size  being  |  in.  or  |  in.  The  smaller  diame- 


220 


MACHINE   DESIGN. 


ters  are  used  with  thin  and  narrow  flanges  and  the  I  in.  size  only 
when  the  thickness  or  stress  requires  it.  Field-rivets  should  not 
be  over  f  in.,  if  possible.  The  selection  of  the  diameter  is,  to  some 
extent,  a  matter  of  judgment. 

The  form  of  the  head  and  point  is  usually  either  spherical,  coun- 
tersunk, or  flattened  to  f  in.  thickness.  Table  LI.  gives  the  pro- 
portions for  spherical  (button-head)  and  countersunk  forms,  the 
formulae  being  : 

Spherical.  Countersunk. 

D  =  \d  +  £",  Angle  of  sides  =  60°, 


in  which  d  =  diameter  of  shank,  D  =  diameter  of  head  or  point, 
H  =  height  of  spherical  or  depth  of  countersunk  head  or  point. 

TABLE  LI. 

PROPORTIONS  OF  RIVET-HEADS. 
(AMERICAN  BRIDGE  Co.) 


Shank. 

Spherical  Heads. 

Countersunk  Heads. 

Diam. 

Diam. 

Height. 

Diam. 

Height. 

in. 

liin- 

A  in. 

r 

t 

lylg. 

it 

A 

: 

it 

I 

i! 

i 

The  conventional  Rivet-signs  used  to  mark  on  the  drawing  the 
character  of  the  head  and  point  are  shown  in  Fig.  93.     To  save 


SJuJ&rets. 


Field  favei 


FltLtte.nt.il  to  £". 


Countersunk 


F%a.\n.. 


FIG.  93. 

time  in  construction,  but  one  size  of  rivet  is  used  throughout  each 
piece,  as  a  plate  girder,  and  the  diameter  of  the  rivet-holes  is  noted 


RIVETED   JOINTS.  221 

on  the  drawing.  The  heads  of  countersunk  rivets  project  usually 
about  \  in.  If  they  are  required  to  be  flush,  they  must  be  chipped. 
The  length  of  rivet-shank  required  for  a  given  joint  is  equal  to 
the  "  grip  "  plus  the  metal  required  to  fill  the  hole  and  form  the 
point.  The  grip  is  the  aggregate  thickness  of  the  connected 
plates  plus  an  allowance  for  irregularity,  of  ^  in.  for  each  place 
where  two  plate-surfaces  meet.  The  diameter  of  the  rivet-holes 
is  Jg  in.  greater  than  that  of  the  rivets.  For,  any  given  grip, 
the  length  of  shank  and  weight  of  spherical  (button)  head  steel 
rivets  may  be  found  from  the  following  data : 

WEIGHT  IN  POUNDS. 


1" 

V 

S" 

r 

i" 

I// 

Shank,  per  in.  of  length. 
Two  rivet-heads. 

.031 
.037 

.056 

.116 

.087 

.222 

•125 
.273 

.170 

•453 

.223 
.780 

3.  THE  SPACING  OF  RIVETS  is  determined  mainly  by  the  re- 
quired strength  at  any  given  point,  tightness,  as  in  pressure  joints, 
not  being  essential.  The  conditions  previously  given  for  the  lat- 
ter, as  to  plate-rupture  and  room  for  the  die,  hold  with  regard  to 
the  minimum  margin  and  pitch.  The  maximum  pitch  in  a  compres- 
sion member  is  fixed  by  the  consideration  that  the  plate  in  a  pitch 
section  is  practically  a  column.  In  general,  also,  the  maximum 
pitch  must  not  be  so  great  as  to  permit  the  entrance  of  moisture 
which  would  rust  and  burst  the  joint.  The  rivets  in  the  ends  of  a 
compression  member  carry  the  full  load  on  the  member  and  are 
spaced  with  this  consideration  in  view.  The  specifications  of  this 
company  as  to  pitch  and  margin  are  : 

The  pitch  of  rivets,  in  the  direction  of  the  strain,  shall  never  exceed  6  inches,  nor 
1 6  times  the  thickness  of  the  thinnest  outside  plate  connected,  and  not  more  than  40 
times  that  thickness  at  right  angles  to  the  strain. 

At  the  ends  of  compression  members,  the  pitch  shall  not  exceed  4  diameters  of  the 
rivet  for  a  length  equal  to  twice  the  width  of  the  member. 

The  distance  from  the  edge  of  any  piece  to  the  centre  of  a  riyet-hole  must  not  be 
less  than  1.5  times  the  diameter  of  the  rivet  nor  exceed  8  times  the  thickness  of  the 
plate  ;  and  the  distance  between  centres  of  rivet-holes  shall  not  be  less  than  3  diame- 
ters of  the  rivet. 

In  structural  work,  the  pitch  of  the  rivets  may  vary  between  the 
minimum  limit,  fixed  by  the  possible  cracking  of  the  plate  in  punch- 
ing or  riveting  and  the  clearance  for  tools,  and  the  maximum  limit 


222 


MACHINE   DESIGN. 


(6"),  determined  by  the  union  of  the  parts  so  that  they  shall  be 
stressed  as  a  whole  and  also  by  the  necessity  for  excluding  mois- 
ture. Table  LII.  gives  various  pitches  for  double  staggered 
riveting  and  for  the  staggered  spacing  of  two  rows  of  rivets  in  the 
two  legs  of  an  angle. 

TABLE  LII. 
STAGGERING  OF  RIVETS.     (AMERICAN  BRIDGE  Co.) 

Distance  c  to  c  of  Staggered  Rivets. 


3A 
3t    |3f    3A3A 


NOTE  :  Values  below  or  to  right  of  upper  zigzag  lines  are  large  enough  for  J  rivets. 
«  "      "  "     "     "  lower      "         "      "       "         "         "•         " 


Minimum  Stagger  for  Rivets. 


J"  Dia 


The  rivet-spacing  for  various  angles  is  given  by  Table  LII  I.  for 
both  longitudinal  and  transverse  pitches.  In -a  "  crimped  angle," 
as  shown  in  Fig.  94,  the  distance,  b,  should  be  i  J  in.  plus  twice 


RIVETED   JOINTS. 


223 


the  thickness  of  chord  angles,  but  never  less  than  2  in.    The  clear- 
ance required  for  |-in.  and  |-in.  rivets  is  shown  by  Fig.  95. 


FIG.  94. 

TABLE  LIII. 
RIVET  SPACING  IN  ANGLES.     (AMERICAN  BRIDGE  Co.) 


I 


Leg. 

G 

Max.  Rivets. 

Leg. 

c/ 

C2 

Max.  Rivets. 

8" 
7 
6 

4 

3^ 

] 

;" 

8" 

7 
6 

5 

3/x 

F 

5 

5 

2 

Jf 

I 

4 
3* 

2i 

2 

When  6"  .£  exceeds  j".    . 

3 

6" 

2£" 

2\" 

Y 

2 

If 

i 

I 

A 

• 

• 

MINIMUM  RIVET  SPACING. 


Size  of  Rivet. 

i" 

I" 

ir 

*" 

i" 

J" 

i" 

i" 

Minimum  Distance. 

I" 

ir 

2// 

2i 

2f 

3X/ 

4.   PUNCHING  AND  RIVETING.  —  The  specifications  of  this  com- 
pany for  steel  railroad  bridges  are  : 

All  riveted  work  shall  be  punched  accurately  with  holes  T\  in.  larger  than  the  size 
of  the  rivet,  and,  when  the  pieces  forming  one  built  member  are  put  together,  the  holes 


224  MACHINE   DESIGN. 

must  be  truly  opposite.  No  drifting  to  distort  the  metal  will  be  allowed  ;  if  the  hole 
must  be  enlarged  to  admit  the  rivet,  it  must  be  reamed. 

All  holes  for  field-rivets,  excepting  those  in  connections  for  lateral  and  sway  bracing, 
shall  be  accurately  drilled  to  an  iron  templet  or  reamed  while  the  connecting  parts  are 
temporarily  put  together. 

In  medium  steel  over  £  in.  thick,  all  sheared  edges  shall  be  planed  and  all  holes 
shall  be  drilled  or  reamed  to  a  diameter  ^  in.  larger  than  the  punched  holes,  so  as  to 
remove  all  the  sheared  surface  of  the  metal. 

The  rivet-heads  must  be  of  approved  hemispherical  shape  and  of  a  uniform  size  for 
the  same  size  rivets  throughout  the  work.  They  must  be  full  and  neatly  finished 
throughout  the  work  and  concentric  with  the  rivet-hole. 

All  rivets  when  driven  must  completely  fill  the  holes,  the  heads  be  in  full  contact 
with  the  surface  or  countersunk  when  so  required. 

Wherever  possible,  all  rivets  shall  be  machine-driven.  Power-riveters  shall  be 
direct-acting  machines,  worked  by  steam,  hydraulic  pressure,  or  compressed  air. 

5.  STRESSES  IN  RIVETED  MEMBERS. — The  built-up  members 
of  framed  structures  are  made  of  rolled  shapes  of  various  forms, 
plates,  angles,  etc.,  joined  by  rivets  which  distribute  and  transfer 
the  stress  developed  by  the  load.  Rivets  should  be  subjected  to 
shearing  and  bearing  stresses  only.  The  connected  parts  resist 
shear,  tension,  compression,  or  compound  stress,  as  their  location 
with  respect  to  the  load  determines. 

Working  Stresses. — The  greatest  permissible  working  stresses 
for  the  parts  of  a  member  vary  with  the  location  of  the  part  and 
the  character  of  its  load.  For  wrought  iron,  general  values  in  Ibs. 
per  sq.  in.  are  :  in  tension,  7,500  ;  in  shear,  6,000.  For  steel,  the 
tensile  stress  ranges  from  10,000  to  17,000  and  the  shearing 
stress  from  6,000  to  11,000.  For  compression  members,  the  per- 
missible stresses  are  those  for  tension,  modified  by  the  relation 
between  the  length  and  least  radius  of  gyration  of  the  section. 
One  formula  of  this  nature  is  quoted  below. 

The  shearing  resistance  in  Ibs.  per  sq.  in.  of  cross-section  for 
rivets  in  single  shear  is  :  iron,  6,000  to  7,500  ;  steel,  7,500  to  12,- 
ooo.  Corresponding  values  of  the  bearing  pressure  are  :  iron, 
12,000  to  15,000 ;  steel,  15,000  to  24,000  Ibs.  per  sq.  in.  upon  the 
projected  area  equal  to  diameter  of  rivet-hole  x  thickness  of  plate. 
For  field-riveting,  the  number  of  rivets  as  calculated  is  increased 
by  10  to  50  per  cent.,  as  a  margin  for  defective  work.  Table  LIV. 
gives  the  shearing  and  bearing  values  of  rivets  for  resistances  of 
11,000  Ibs.  (single  shear)  and  22,000  Ibs.  per  sq.  in.  respec- 
tively. 


RIVETED  JOINTS. 


225 


i 


ill 


M       N 


88  8 


a 

10  VO     t^  00 


O  Q  O     Q     O 

p-c  VO  t^  vO     HI 

N  M  ro  OO    v£) 

M  C")  CO   -^-  \O 


rO  OO    00     f> 


10  o    ^o  O    >o 
t-.   0    M    tr>  t-. 

rO    up  vq     t^  00 


i! 


II 


M  ^ 

•c  ^ 
S  j) 


226 


MACHINE   DESIGN. 


The  following  extracts  from  specifications  refer  to  the  require- 
ments of  this  company  as  to  working  stresses  in  steel  railroad 
bridges  : 

All  parts  of  the  structure  shall  be  so  proportioned  that  the  sum  of  the  maximum 
loads,  together  with  the  impact,  shall  not  cause  the  tensile  strain  to  exceed  :  on  soft 
steel,  15,000  Ibs.  per  sq.  in.;  on  medium  steel,  17,000  Ibs.  per  sq.  in. 

*  *  *  For  compression  members,  these  permissible  strains  of  15,000  and  17,000 
Ibs.  per  sq.  inch  shall  be  reduced  in  proportion  to  the  ratio  of  the  length  to  the  least 
radius  of  gyration  of  the  section  by  the  following  formulae  : 

15,000 

I1        ''  (128) 


For  soft  steel,  p  = 


For  medium  steel, 


17,000 


u,ooor2 


(129) 


where  /  =  permissible  working  strain  per  sq.  in.  in  compression  ;  /  =  length  of  piece 
in  inches,  centre  to  centre  of  connection  ;  r  =  least  radius  of  gyration  of  the  section  in 
inches. 

*  *  *  The  shearing  strain  on  rivets,  bolts,  or  pins  per  sq.  in.  of  section  shall  not 
exceed  n,ooo  Ibs.  for  soft  steel  and  12,000  Ibs.  for  medium  steel  ;  and  the  pressure 
upon  the  bearing  surface  of  the  projected  semi-intrados  (diameter  X  thickness)  of  the 
rivet,  bolt,  or  pin  hole  shall  not  exceed  22,000  Ibs.  per  sq.  in.  for  soft  steel  and  24,000 
Ibs.  for  medium  steel.  In  field-riveting,  the  number  of  rivets  thus  found  shall  be  in- 
creased 25  per  cent.,  if  driven  by  hand,  but  10  per  cent,  if  driven  by  power. 

*  The  shearing  strain  in  web-plates  shall  not  exceed  9,000  Ibs.  per  sq.  in.  for 
soft  steel  and  10,000  Ibs.  per  sq.  in.  for  medium  steel ;  but  no  web  plate  shall  be  less 
than  Jljin.  in  thickness. 

I 


FIG.  96. 

6.  DISTRIBUTION  OF  STRESSES. — The  character  and  distribution 
of  the  stresses  in  a  member  depend  upon  the  function  of  the  latter. 
The  Plate-Girder  is  a  fairly  comprehensive  example  of  the  prin- 
ciples of  design  in  riveted  structural  work.  As  shown  in  Fig.  96, 


RIVETED   JOINTS.  22? 

it  consists  essentially  of  a  web-plate,  W,  and  four  angles,  L,  ex- 
tending from  end  to  end.  To  these  may  be  added,  at  top  and 
bottom,  a  flange-plate,  C,  of  partial  or  full  length,  and,  if  required, 
one  or  more  flange-plates,  Cv  traversing  the  section  in  which  the 
magnitude  of  the  bending  moment  makes  necessaiy  the  additional 
flange-area.  These  plates  are  all  of  the  same  width,  which  is  that 
of  the  girder.  The  upper  and  lower  flanges  are  similar,  excepting 
that  one  plate  of  the  latter  is  usually  thicker  to  make  up  for  the 
loss  in  net  plate-section  due  to  rivet-holes.  The  parts  are  joined 
by  rows  of  rivets,  r,  passing  through  web  and  angles  and  rows,  rv 
through  angles  and  flange-plates.  As  a  rule,  these  are  single 
rows.  The  method  of  design  is  indicated  briefly  below.* 

Length,  Width,  Depth. — The  length,  /,  is  the  distance  between 
the  centres  of  the  end  -bearings.  Since  the  upper  flange  is  in  com- 
pression, it  may  buckle  if  weak.  Hence,  if  the  unsupported  length 
of  the  girder  exceeds  1 6  to  20  times  its  width,  b,  the  girder  should 
be  given  lateral  support.  The  depth,  h,  is  the  distance  between 
the  centres  of  gravity  of  the  cross-sections  of  the  flanges,  each  of 
the  latter  being  made  up  of  two  angles  and  the  attached  flange- 
plates.  The  effective  depth  may  be  taken,  without  material  error, 
as  that  of  the  web-plate.  To  avoid  excessive  deflection,  the  least 
depth  should  be  Jfr  to  tV  °^  t^ie  sPan-  ^or  ^e  economical  depth, 
with  regard  to  weight,  Mr.  C.  W.  Bryan,  C.E.,  gives  the  follow- 
ing formulae  :  f 

Neglecting  moment  of  resistance  of  web  to  bending : 

x=  1.27 
Considering  moment  of  resistance  of  web  to  bending  : 

x=i.46^~;     (131) 
in  which, 

x  =  depth  of  girder,  ins. ; 

tn=  centre-moment,  inch-lbs.,  from  dead  and  live  loads ; 

f-=  allowable  fibre-stress  on  flanges,  Ibs.  per  sq.  in.  ; 

/  —  thickness  of  web,  ins. 

*  For  detailed  investigation,  see  Burr:  "  Elasticity  and  Resistance,"  etc.,  1897,  p. 
578  ;  Johnson,  Bryan,  Turneaure  :  "Modern  Framed  Structures,"  1901,  p.  292. 
-(-"Modern  Framed  Structures,"  1901,  p.  299. 


228  MACHINE    DESIGN. 

Moments,  Vertical  Shear,  Flange-stress.  —  The  external  forces 
acting  on  the  girder  are  the  loads  and  the  reactions  at  the  sup- 
ports. These  are  transmitted  directly  to  the  web  by  vertical 
angles,  D,  riveted  to  the  web  at  the  supports  and  under  concen- 
trated loads  and  by  the  rivets,  r,  of  the  compression  flange.  The 
vertical  shear  produced  in  the  web  by  the  loads  acts  upon  the 
rivets,  r,  of  both  flanges  with  a  leverage  equal  to  the  pitch  of  the 
rivets,  and  thus  develops  bending  stress  in  the  flanges.  Since 
the  parts  are  so  bound  together  that  the  girder  bends  as  a  whole, 
bending  stress,  in  addition  to  shear,  acts  in  the  web.  Two  methods 
of  design  are  used  :  Either  to  assume  that  the  web  is  subjected 
to  vertical  shear  only  and  proportion  the  flanges  for  the  full  bend- 
ing stress;  or  —  and  correctly  —  to  allow  for  the  resistance  to 
bending  of  the  web  and  design  the  flange-area  for  the  remainder 
of  the  load. 

Let  A  be  the  sectional  area  of  the  angles  and  plates  (web  not 
included']  forming  one  flange  at  any  given  point  in  the  girder  and 
5  the  mean  unit  working  stress  over  that  area.  Then,  A  x  S  is  the 

total  load  or  horizontal  bending  stress  on  the  flange  and  A-S  x  -  — 

resisting  moment  of  this  stress  about  the  neutral  axis  of  the  girder. 
Assuming  A  and  5  as  the  same  for  both  flanges  and  neglecting 
the  bending  stress  on  the  web,  the  external  bending  moment  at 
the  given  point  =  resisting  moment  of  girder  at  that  point  ;  or, 


(132) 


Flange-stress  =  A.S.  =  -j-\  (  *  3  3) 


Flange-area  =  ^  =  —  .  (134) 


The  web-section  is  that  of  a  rectangular  beam  of  depth,  h,  and 
breadth  equal  to  the  thickness,  t.     Hence,  its  resistance  to  bend- 

S.th* 
ing  is      ~        To  allow  for  the   reduced  section   due  to  vertical 


RIVETED   JOINTS.  229 

rows  of  rivet-holes  the  6  is  replaced  by  8.     Hence,  considering 
the  resistance  of  the  web  to  bending  stress  : 

(135) 


Flange  -stress  =  A.S  =  -    --  ~  ;  (136) 


M       t.h 
Flange-area  =  A  =  -       -  —  •  (137) 


For  steel  girders  in  buildings,  the  usual  unit  flange-stress,  S,  is 
15,000  Ibs.  per  sq.  in.  and  the  unit  shearing-stress,  Se,  on  the  web 
is  7,000  to  1  1,000  Ibs.  per  sq.  in. 

FLANGE-AREA,  ANGLES,  FLANGE-PLATES.  —  The  required  flange- 
area  at  any  given  point  in  the  girder  may  be  found  from  (134)  or 
(137).  The  area  found  thus,  serves  for  the  compression  flange 
which  is  assumed  as  not  weakened  by  the  rivet-holes,  since  the  rivets 
should  about  fill  the  latter.  The  resistance  of  plates  and  angles 
in  the  tension  flange  is  that  of  their  net  section.  The  two  rivet- 
rows,  rv  are  opposite  each  other  ;  but  1\  is  staggered  with  regard 
to  r.  Hence,  the  net  section  of  a  cover  or  flange-plate  is  (b  —  2d) 
x  thickness  and  the  net  area  of  an  angle  =  gross  area  —  d  x 
thickness.  The  diameter,  d,  is  that  of  the  rivet  plus  ^  in.,  to  allow 
for  enlarged  hole  and  effects  of  punching.  The  increased  area 
required  in  the  tension  flange  is  added  by  thickening  one  of 
the  flange  -plates  or  by  calculating  for  the  tension-flange  and  mak- 
ing the  area  of  both  flanges  the  same.  The  flange-area  may  be 
calculated  for  different  points  in  the  girder  or  it  may  be  found 
graphically  as  shown  in  Fig.  c>6a,  which  is  the  bending  moment 
diagram  for  a  concentrated  load  at  the  centre  of  the  girder.  The 
maximum  bending  moment,  M,  should  be  equal  to  the  sum  of  the 
individual  resisting  moments  R.L,  R.C,  R.CV  of  the  angles,  L,  and 
the  flange  -plates,  C  and  Cv  i.  e.,  on  the  same  scale,  M=  R.L  + 
R.C  +  R.  Cr  Hence,  at  a,  the  full  section  will  be  required  ;  at  c, 
that  of  L  and  C  ;  and  at  c  that  of  L  only.  These  theoretical  lengths 
of  flange  -plates  are  increased  somewhat,  as  will  be  shown  later. 
In  general,  .not  less  than  50  per  cent,  of  the  maximum  flange-area 
should  be  in  the  angles,  since  the  thinner  the  flange-plates,  the 


230 


MACHINE    DESIGN. 


less  their  leverage  through  the  rivets  on  the  angles,  both  vertically 
and  with  regard  to  the  centre  of  gravity  of  the  latter. 

The  sectional  areas  of  various  angles  are  given  in  Table  LV. 
The  centre  of  gravity  of  a  given  flange-area  should  be  as  far  as 
possible  from  the  neutral  axis  of  the  girder  in  order  to  give  the 
maximum  resisting  moment  to  bending  and  the  maximum  breadth 
of  the  area  should  be  as  great  as  the  conditions  permit  in  order  to 
strengthen  the  girder  against  buckling  or  lateral  yielding.  Hence, 
the  angles  should  have  unequal  legs  with  the  longer  horizontal. 
The  thickness  of  the  angle  should  be,  approximately,  that  of  the 
web-plate. 

TABLE  LV. 

ANGLES:  SECTIONAL  AREAS  (SQ.  INS.). 
(AMERICAN  BRIDGE  Co.) 


Size. 

i" 

A" 

i" 

A" 

1" 

A" 

*" 

A" 

1" 

ii" 

J" 

il" 

i" 

IB"    |     i" 

8"  X  8" 

7.76  8.76 

976 

10.76 

11.47 

12.47 

13-47 

I4.50  15.53 

6   X6 

4-35 

5-09 

5-79   6.47 

7.18    7.79   8.47 

9.121  9.82  10.56 

5    X5 

3.62 

4.21 

4-79 

5-35 

5-91 

6.47    7.00 

7.53  8.06 

8.65 

4   X4t 

2.41 

2.88 

3-32 

3-76 

4.21 

4.65 

5.06 

5-47 

2.09 

2.50 

2.88 

3-26 

3-65 

4-03 

2    X2* 

1-44 

1-79 

2.12 

2.44 

2.76 

3-06 

3.38 

1.32 

1.65 

1-94 

2.26 

2-53 

2\  X  22 

0.91 

1.  21 

1-47 

1.74 

2.03 

2.29 

2?  X  2? 

0.79 

1.06 

1.32 

1-59 

2     X  2 

0.74 

0.94 

1.18 

1.41 

if  X  if 

0.62 

0.82 

1.03  j  1.21 

i\  X  ij 

0-35 

0-53 

0.71 

0.85     1.03 

I  jf  X  IT 

0.29 

o.44 

0.59 

i   Xi 

0.24 

Q.35 

0.44 

8  X6 

1  6.76   7.59 

"84! 

9-32 

~9^94 

10.76  11.62  12.5013.41 

7   X  3z 

5-oo  15.59   6.18 

6.76 

7.29   7.85    8.41    8.97    9.56 

6   X4 

3-59 

4.21 

4-79 

5-32 

5.91 

6.47 

7.00   7.53;  8.06   8.65 

6X3* 

3-41 

4.00 

4.56 

5-03 

5.59    6.12 

6.65    7.21 

7-79 

8.4I 

5    X4 

3-24 

3.76 

4-29 

4.76 

5-26    5.76 

6.26 

5    X3* 
5   X3 

2-56 
2.41 

3-03 
2.85 

3.53   4.00   4.47 
3.29   3.76   4.18 

4-94  j  5-41 
4.62     5.06 

5-88 
5.50 

4   X3i 

2.26 

2.68   3.09 

3-5o 

3-91 

4-32  1  4JI 

5-12 

4xX3 

2.09 

2.50   2.88 

3-26 

3.65 

4.06 

1.94 

2.29  j  2.68  j  3.03 

3-41 

3-79 

3  i  X  2i 

1.44 

1.79 

2.12  1  2.44 

2.76 

3    X  ^ij 

1.32 

1.62 

1.94     2.26 

2.56 

2JX2 

0.79 

i.  06 

1.32 

i-59 

1.82 

2.06 

2X4 

0.62 

0.85 

1.  06 

1.26 

2     XI* 

0.56 

0.76 

0.97 

1.  15 

- 

In  general,  the  aim  in  design  should  be  to  make  the  girder 
as  deep  and  the  angles  as  heavy  as  possible  in  order  to  reduce 
the  thickness  of  the  plates  and  their  consequent  leverage  through 


RIVETED   JOINTS.  231 

the  rivets  on  the  angles.  In  compression,  one  plate -is  better 
than  two  of  the  same  aggregate  thickness.  To  increase  the  re- 
sistance to  buckling,  the  plates  of  the  compression  flange  may  be 
made  the  full  length  of  the  girder.  Since  the  stress  is  transmitted 
to  the  plates  by  the  flange  rivets,  rv  the  width  of  the  plates  outside 
of  those  rows  is  limited  by  the  necessity  for  an  approximately  uni- 
form distribution  of  stress. 

Web-plate,  Stiffeners.  —  The  thickness  of  the  web-plate,  W,  must 
be  such  as  to  provide  for  the  maximum  vertical  shear  at  the  sup- 
ports and  to  give  sufficient  bearing  area  for  the  rivets  joining  the 
web  and  angles  without  making  the  pitch  of  the  rivets  smaller  than 
the  minimum  allowable.  The  minimum  thickness  of  web  is  ^  in. 
for  light  work.  In  railway  bridges,  no  web  less  than  f  in.  thick 
should  be  used. 

The  load  on  the  web  not  only  produces  vertical  shear  and  bend- 
ing stress  but  also  tends  to  make  the  plate  yield  vertically  by 
buckling.  The  latter  is  prevented  by  pairs  of  vertical  angles  or 
stiffeners,  B,  riveted  to  the  web.  If  the  thickness  of  the  latter  is 
less  than  g1^  of  its  depth,  the  stiffeners  are  placed  at  intervals  not 
greater  than  the  depth  of  the  girder  throughout  the  length  of  the 
latter,  with  a  maximum  spacing  of  5  ft.  Angles  for  stiffening  solely 
may  be  made  very  light.  They  should  bear  against  both  upper 
and  lower  flange  angles  and  the  web,  being  bent  inward  to  the  lat- 
ter or  left  straight  and  a  filling  piece  interposed. 

At  the  supports  and  under  concentrated  loads,  as  at  D,  the  stiff- 
eners have  the  further  function  of  transferring  the  external  loads 
to  the  web-plate.  The  rivets  passing  through  them  should  have 
a  strength  sufficient  for  this.  Hence,  in  addition  to  the  fitting  and 
bearing  as  above,  these  transferring  stiffeners  should  be  broad 
enough  to  give  space  for  the  rivets  and  thick  enough  to  prevent 
the  pressure  on  the  rivets  and  of  the  stiffener  on  the  lower  flange- 
angle  from  exceeding  the  allowable  bearing  stress. 

Riveting.  —  The  rivets  r,  and  rv  are  in  double  and  single  shear 
respectively  and  both  are  under  bearing  pressure  which  must  be 
computed  for  the  least  bearing  surface  in  either  direction  of  stress. 
The  strength,  s,  of  a  rivet  is  its  least  resistance  under  either  of  the 
two  stresses  to  which  it  is  subjected.  The  vertical  shear  in  the 
web  acts  through  the  rivets,  r,  on  the  flanges,  bending  the  latter. 
Considering  only  bending  stress,  the  required  number  of  the  rivets, 
r,  depends  upon  their  diameter  and  the  magnitude  of  the  bending 


232  MACHINE   DESIGN. 

moment.  Let  Me  be  the  bending  moment  on  the  tension  flange  at 
E.  The  flange-stress  Af.S  divided  by  the  strength,  s,  will  give 
the  number  of  rivets  for  Me  from  E  to  either  support.  Again, 
the  increase  of  moment  between  E  and  F  is  Mf  —  Me  and  the  in- 
crease of  flange-stress  is  S(Af  —  Ae).  The  latter  divided  by  s  gives 
the  number  of  rivets  to  be  added  between  E  and  F,  the  total  num- 
ber thus  far  being  that  on  either  side  of  F  for  the  moment  M . 
In  general,  the  number,  N,  of  rivets  required  on  each  side  for  a 
moment,  M,  is : 

N~~  (138) 

Again,  from  the  relation  between  the  bending  moment  and  the 
vertical  shear,  F,  we  have,  for  an  elementary  length,  dx : 

V=d~-->  Fx  dx=dM, 
dx 

i.  e.,  the  vertical  shear  at  the  left  of  dx  acts  with  a  leverage  dx  to 
produce  the  increment  of  moment,  dM.  Let  the  length  of  the 
section  be  the  pitch,  /,  between  two  rivets,  a  at  the  left  and  b  at 
the  right.  Then,  if  Ma ,  Aa,  Mb,  and  Ab  be  the  respective  moments 
and  flange-areas,  we  have,  neglecting  resistance  to  bending  of  web : 

Vxp  =  Mb-Ma  =  h  [AbS  -  AaS]  =  h.s  • 

h.s 
/=    F>  (139) 

since  the  rivet,  b,  must  resist  the  increment  of  flange-stress 
required  in  the  distance,  p. 

In  the  upper  or  compression  flange,  in  addition  to  the  horizon- 
tal bending-stress,  the  rivets,  r,  are  subjected  to  vertical  stress  from 
the  loads  transmitted  by  them  to  the  web.  These  loads  are  :  the 
weight  of  the  girder,  the  uniform  load  if  any,  and  any  concen- 
trated load  which  is  not  provided  for  fully  by  transmitting  angles, 
D.  Let  w  be  the  sum  of  these  loads  per  inch  of  length  of  gir- 
der at  the  section  considered.  Then  /  x  w  will  be  the  vertical 
load  upon  the  pitch  section  and  on  one  rivet.  From  (139)  the 

horizontal  load  due  to  any  pitch,  /,  is  -.  -  .  The  final  stress  upon 
the  rivet  will  be  the  resultant  of  these  two  loads  which  are  normal 


RIVETED   JOINTS.  233 

to  each  other  and  this  resultant  must  not  exceed  the  strength,  s, 
of  the  rivet.      Hence,  neglecting  resistance  to  bending  of  web : 


(I4o) 

p  and  h  being  expressed  in  inches  and  s,  V,  and  zv  in  Ibs. 

From  (139)  and  (140)  the  pitches  in  both  flanges  of  rivets,  r, 
may  be  obtained.  If  the  bending  resistance  of  the  web  be  con- 
sidered, equations  (139)  and  (140)  must  be  modified  in  accordance 
with  the  terms  of  (136).  The  shear  is  greatest  and  the  pitch  least 
at  the  supports,  both  varying  in  some  degree  at  every  section.  In 
practice,  the  minimum  pitch  required  is  generally  preserved  until 
the  maximum  (6  in.)  can  be  used.  The  number  of  rivets  in  the 
tension  flange  will  be  less  than  that  in  the  upper  angle,  but,  for  con- 
structive reasons,  rivets  inserted  below  should  be  in  line  vertically 
with  those  above.  When  the  moment  of  resistance  of  the  web 
to  bending  is  considered,  the  pitch  formulae  should  be  changed  to 
include  this  factor. 

The  pitch  of  the  rivets,  rlt  joining  the  flange-plates  to  the  angles 
is  6  in.  excepting  at  the  ends  of  the  plates.  The  latter  are  ex- 
tended beyond  the  theoretical  limits  sufficiently  to  provide  space 
for  enough  rivets  in  the  two  rows  to  carry  the  load  on  the  plate 
in  each  case,  the  pitch  of  these  rivets  being  4  diameters.  Thus, 
theoretically,  the  plate,  C,  ends  at  c.  The  load  on  this  plate  is  ap- 
proximately the  product  of  its  net  cross-section  and  the  working 
stress.  Dividing  this  load  by  the  strength  of  one  rivet,  we  have 
the  total  number  of  rivets  in  both  rows  to  be  driven  between  e  and 
the  end,  ev  of  the  plate. 

The  following  extracts  from  the  specifications  of  this  company 
for  steel  railroad  bridges  cover  the  points  discussed  above : 

"  Girders  shall  be  proportioned  on  the  assumption  that  £  of  the  gross  area  of  the  web 
is  available  as  flange-area.  The  compressed  flange  shall  have  the  same  sectional  area  as 
the  tension  flange  ;  but  the  unsupported  length  of  flange  shall  not  exceed  16  times  its  width. 

"  In  calculating  shearing  strains  and  bearing  strains  on  web  rivets  of  plate-girders,  the 
whole  of  the  shear  acting  on  the  side  next  the  abutment  is  to  be  considered  as  being 
transferred  into  the  flange  angles  in  a  distance  equal  to  the  depth  of  the  girder. 

"The  web  shall  have  stiffeners  riveted  on  both  sides,  with  a  close  bearing  against 
upper  and  lower  flange  angles,  at  the  ends  and  inner  edges  of  bearing  plates  and  at  all 

*"  Modern  Framed  Structures,"  1901,  p.  306. 


234 


MACHINE    DESIGN. 


points  of  local  and  concentrated  loads  ;  and  also  when  the  thickness  of  the  web  is  less 
than  -fa  of  the  unsupported  distance  between  flange-angles,  at  points  throughout  the 
length  of  the  girder  generally  not  farther  apart  than  the  depth  of  the  full  web-plate, 
with  a  maximum  limit  of  5  ft. 

«  *  *  *  AH  joints  in  riveted  work,  whether  in  tension  or  compression  members  must 
be  fully  spliced. 

«  *  *  *  Web-plates  of  girders  must  be  spliced  at  all  joints  by  a  plate  on  each  side  of 
the  web,  not  less  than  f  in.  thick,  capable  of  transmitting  the  full  strain  through  splice 
rivets. 

"The  flange-plates  of  all  girders  must  be  limited  in  width  so  as  not  to  extend  beyond 
the  outer  lines  of  rivets  connecting  them  with  the  angles  more  than  5  in.  or  more  than 
8  times  the  thickness  of  the  first  plate.  Where  two  or  more  plates  are  used  on  the 
flanges,  they  shall  either  be  of  equal  thickness  or  shall  decrease  in  thickness  outward 
from  the  angles." 

TABLE  LVI. 

RIVETED  vs.  BOLTED  JOINTS. 

(LAP  JOINTS.) 

r*-      7       — »> 


0 

o—  |  

i 

in/ 


Joints  A. 
Joints  B. 

Double  Riveted. 
Double  Bolted. 

Treble  Riveted. 
Treble  Bolted. 

Quadruple  Riveted. 
Quadruple  Bolted. 

Rivets  or  bolts,  Diam. 

\" 

I" 

\" 

"     "      No. 

2 

3 

4 

"     "      Pitch. 

3T/ 

3" 

Plates,  width. 

tji" 

1" 

thickness. 

I/? 

i// 

V 

lap. 

Y' 

10" 

'37' 

tensile  stress  per  sq.  in. 

at  failure  for  : 

Iron  rivets. 

26,  1  20  Ibs. 

24,310  Ibs. 

26,450  Ibs. 

Steel  rivets. 
Iron  bolts. 

26,990    " 
18,690    » 

29,590    " 
18,090    " 

28,820    " 
20,470    " 

Steel  bolts. 

21,110     " 

21,460    " 

22,060    " 

Failure,  in  all  cases,  by  shearing  rivets  or  bolts. 

7.  BOLTS.  —  For  facility  in  erection  or  in  cases  where  a  rivet 
would  be  in  tension,  bolts  are  used  as  permanent  fastenings  in  some 
parts  of  structural  work.  For  full  strength  they  require  to  be 
finished  and  fitted  accurately  in  drilled  holes.  Tables  LVI.  and 
LVII.  give  comparative  tests  —  made  for  the  Berlin  Iron  Bridge 
Co.  at  the  Watertown  Arsenal  in  1896  —  of  riveted  and  bolted 
single-  and  double-shear  joints  with  punched  holes.  The  plates 


RIVETED   JOINTS. 


235 


were  of  steel ;  diameter  of  punch,  i|  in.,  of  die,  £  in.  ;  chain-rivet- 
ing, the  "pitch"  in  the  tables  being  the  distance  between  the 
rows.  The  test-piece  consisted  of  a  section  of  the  joint  contain- 
ing one  rivet  in  each  row.  The  joints  were  similar  throughout, 
excepting  that  the  rivets  in  A  and  C  were  replaced  in  B  and  D  by 
through  bolts  and  nuts. 

TABLE  LVII. 

RIVETED  vs.  BOLTED  JOINTS. 
(ONE  WEB  AND  Two  COVER-PLATES.) 


O      G~ 


'T 


/tv 


Joints  C. 
Joints  D. 

Double  Riveted. 
Double  Bolted. 

Treble  Riveted. 
Treble  Bolted. 

Quadruple  Riveted. 
Quadruple  Bolted. 

Rivets  or  bolts,  Diam. 

I" 

f" 

f" 

"      "     No. 

2 

3 

4 

"      "      Pitch. 

•3" 

3" 

3" 

PI    es,  width. 

4" 

V 

8" 

thickness. 

|  and  f  " 

fandf" 

|  and  \" 

lap. 

1" 

10" 

13" 

tensile     stress. 

(web)  per  sq.  in.  at 

failure  for  : 

Iron  rivets. 

29,670  Ibs. 

28,520  Ibs. 

28,470  Ibs. 

Steel      " 

29,540    " 

31,040    " 

28,970    " 

Iron  bolts. 

18,000    " 

17,720    " 

18,990    " 

Steel     " 

20,050    " 

25,010    " 

23,440    " 

Manner  of  failure  for  : 

Iron  rivets. 

Sheared  rivets. 

Sheared  rivets. 

Sheared  rivets. 

Steel     " 

Fractured  web  plate. 

K          « 

Fractured    covers 

through  rivet  holes. 

Iron  bolts. 

Sheared    bolts,    both 

"       bolts. 

Sheared  bolts. 

planes. 

Steel     " 

Sheared      bolts,     one 

«           « 

K                    « 

plane. 

53.     Riveted  Joints,  Hull  Plating. 

The  hull  of  a  ship  is  essentially  a  girder  constructed  to  bear 
a  given  maximum  load  with  various  modes  of  support.  Hence 
the  principles  which  govern  the  design  of  structural  work  in 


236  MACHINE   DESIGN. 

general  apply  to  the  proportion  and  connection  of  the  members  of 
hull-framing.  In  the  joints  of  the  outside  plating  and  those 
of  the  double  bottom,  bulkheads,  etc.,  there  is  the  further  re- 
quirement of  tightness  against  water-pressure.  Since  the  lat- 
ter is,  in  any  event,  but  moderate,  these  joints  hold  an  interme- 
diate position,  with  respect  to  tightness,  between  those  of  general 
structural  work  and  the  seams  of  steam  boilers. 

In  outside  plating,  the  longitudinal  seams  are  lapped  except 
where  flush  work  is  required.  The  transverse  seams  are  butt 
joints  with  single  straps.  Rivet-points  are  countersunk  and 
chipped  and  all  seams  are  calked.  The  riveting  is  done  either  by 
hand-work,  or  by  portable  hydraulic  or  pneumatic  machines  car- 
ried on  a  gantry  which  spans  the  ship,  or  by  the  pneumatic  rivet- 
ing hammer  which,  with  its  frame  and  pneumatic  "  holder-on," 
forms  a  readily  portable  combination  operated  by  two  men.  The 
latter  method  for  hull-riveting  is  meeting  wide  adoption  in  the 
United  States.  With  regard  to  its  cost  and  results  as  compared 
with  hand-work,  Edwin  S.  Cramp,  Esq.,  Vice  President  of  the 
William  Cramp  and  Sons  Ship  and  Engine  Building  Co.,  says  : 

"  We  have  found  that  the  use  of  these  tools  results  in  an  increase  of  operating  expenses 
and  a  decrease  in  labor-charges,  with  a  net  saving  of  about  ten  per  cent,  over  the  cost 
of  hand-riveting.  The  quality  of  the  work  done  and  the  speed  with  which  it  is  done 
are  increased  to  a  great  extent." 

Rivets  are  usually  of  steel.  Up  to  |  in.  diameter  they  should 
be  riveted  cold,  since  the  rivet-blank  of  small  size  not  only  cools 
very  quickly  but,  proportionately,  wastes  much  more  rapidly  by 
oxidation  and  scaling.  For  cold-riveting,  the  steel  should  be  soft 
and  ductile  as  the  harder  metal  of  higher  tensile  strength  becomes 
brittle  and  untrustworthy  when  thus  worked.  The  countersunk 
points  used  in  shell  plating,  while  more  costly  and  giving  a  re- 
duced net  section  of  plate,  have  two  great  advantages  :  Their  use 
removes  much  of  the  metal  injured  in  punching  the  holes  and  they 
add  no  weight  to  that  of  the  full  plate,  since  they  are  chipped  flush. 
Weight-saving  without  reduction  of  strength  is  a  matter  of  impor- 
tance in  ships,  especially  in  men-of-war,  since  useless  weight  is 
but  so  much  unprofitable  load  to  be  transported  during  the  life  of 
the  ship.  Rivets  form  a  very  considerable  proportion  of  the  total 
weight  of  the  hull.  Naval  Constructor  J.  H.  Linnard,  U.  S.  Navy, 
gives,*  for  the  U.  S.  Armored  Cruiser  Brooklyn  (9,270  tons),  the 

*  Trans.  Soc.  Naval  Architects  and  Marine  Engineers,  Vol.  IV. 


RIVETED   JOINTS. 


237 


total  weight  of  rivets  driven  as  upward  of  330,000  Ibs.,  of  which 
weight  from  ^  to  ^  is  in  the  rivet-heads  and  points.  The  rivet 
blank  will  have  a  better  fit  in  punched  holes  which  are  not  counter- 
sunk, if  coned  under  the  head  as  shown  in  Fig.  97. 


Countersunk  or-  Plug  ffeacls. 
ClatsA  ClnssR 


Panffead. 
Class  A.          Class  B. 


JButttm.  //ecul.  £uiton  or  S'nap  Point. 

Class  A 


Jeyo  Rivet*. 


Template  fir  Cmcnt 

F;G.   97. 


I .  U.  S.  NAVAL  PRACTICE. —  The  following  extracts,  relating  to 
hull-riveting  in  general,  are  taken  from  the  Specifications  (1899) 
of  the  Bureau  of  Construction  and  Repair,  U.  S.  Navy. 

PLATE  AND  RIVET  METALS  : 

SHIP  PLATES  AND  SHAPES. 

26.  Kind  of  Material.  —  Plates  and  shapes  shall  be  of  steel  or  nickel  steel,  made 
by  the  open  hearth  process,  and  must  not  show  more  than  six  one-hundredths  (.06)  of 
one  per  cent,  of  phosphorus,  nor  more  than  four  one-hundredths  (.04)  of  one  per  cent. 


238  MACHINE   DESIGN. 

of  sulphur  for  acid  steel;  and  not  more  than  four  one-hundredths  (.04)  of  one  per 
cent,  of  phosphorus,  nor  more  ihanfottr  one-hundredths  (.04)  of  one  per  cent,  of  sul- 
phur for  basic  steel.  The  material  shall  be  of  the  best  composition  in  all  other  respects. 

At  the  option  of  the  manufacturer  the  material  may  be  annealed. 

The  material  will  be  classified  in  three  standard  grades  according  to  its  characteris- 
tics and  the  purposes  for  which  intended.  These  grades  will  be  known  as  ( I )  soft  or 
flange  steel,  (2)  medium  steel  and  (3)  hard  steel. 

The  following  are  the  minimum  requirements  of  each  grade  of  steel : 


Grade. 

Tensile  Strength. 

Elongation. 

Cold  Bend. 

Quench  Bend. 

Soft  or  flange 

50,000  Ibs. 

30  per  cent. 

1  80°  flat. 

1  80°  flat. 

steel. 

Medium  steel. 

60,000  Ibs. 

25  per  cent. 

For  plates  below  For  plates  below  f 

\    inch  in  thick- 

inch in  thickness; 

ness  :     I  80°    flat 

1  80°  to  diameter 

for  longitudinal  ; 

of  \\  thicknesses 

1  80°  to  diameter 

for   longitudinal  ; 

of  I  thickness  for 

1  80°  to  diameter 

transverse.      For 

of  2.\  thicknesses 

plates    above     \ 

for  transverse. 

inch  in  thickness, 

For  plates  above 

the  bends  will  be 

f  inch   in  thick- 

1 80°  to  a  diame- 

ness,   the    bends 

ter  of  I  thickness 

will  be  1  80°  to  a 

for    longitudinal, 

diameter     of    \\ 

and  2  thicknesses 

thicknesses     for 

for  transverse 

longitudinal,  and 

specimens. 

2\  thicknesses  for 

transverse   speci- 

mens. 

Hard  steel. 

75,000  Ibs. 

1  8  per  cent. 

1  80°  to  a  diameter 

No  quench  bend. 

of  ij  thicknesses 

for  longitudinal  ; 

1  80°  to  a  diameter 

of  3    thicknesses 

for  transverse. 

PROTECTIVE  DECK  PLATING. 

38.  The  lower  courses  of  plating  for  the  protective  deck  will  be  of  steel  of  the  quali- 
ties of  ship  plate,  and  shall  be  inspected  accordingly. 

39-  The  upper  course  of  plating  of  protective  deck  shall  be  of  nickel  steel,  contain- 
ing about  three  and  a  quarter  (3^)  Per  cent-  °f  nickel,  not  more  than  six  one-hun- 
dredths (.06)  of  I  per  cent,  of  phosphorus,  nor  more  than  four  one-hundredths  (.04) 
of  I  per  cent,  of  sulphur,  and  be  of  the  best  composition  in  all  other  respects.  All 
these  plates  shall  be  oil-  or  water-tempered  and  annealed. 

All  rivets  are  of  steel  whose  characteristics  are  : 


HULL  RIVETS. 

43.  Kind  of  Material.  —  Steel  for  hull  rivets  shall  be  made  by  the  open-hearth 
process,  and  not  show  more  than  five  one-hundredths  (.05)  of  one  per  cent,  of  phos- 
phorus, nor  more  than  four  one-hundredths  (.04)  of  one  per  cent,  of  sulphur,  and  be 
of  the  best  composition  in  other  respects. 


RIVETED   JOINTS.  239 

44.  A  whole  heat  or  part  thereof  may  be  rolled  into  rivet  rods,  and  from  each  size 
rolled  six  (6)  tensile  tests  shall  be  taken  at  random,  each  from  a  different  bar  as  finished 
at  the  rolls.     When  lots  smaller  than  five  tons  are  rolled,  one  test  piece  shall  be  taken 
from  each  size  for  every  ton  or  fraction  thereof. 

45.  Rods  from  which  rivets  are  to  be  made  of  a  diameter  of  one  half  (£)  inch  or  less 
shall  be  tested  in  the  diameter  of  the  finished  rivet.     These  rods  shall  show  a  tensile 
strength  of  not  less  than  58,000  pounds  per  square  inch  and  an  elongation  of  not  less 
than  28  per  cent. 

46.  Rods  from  which  rivets  are  to  be  made  of  a  diameter  above  one  half  (£)  inch 
shall  be  tested  with  specimens  of  the  same  diameter  as  the  finished  rivet,  when  practic- 
able, and  shall  show  the  same  tensile  strength  as  the  smaller  rivets  and  an  elongation 
of  not  less  than  29  per  cent.     Specimens  from  these  rods  shall  be  of  the  maximum  cross 
section  within  the  capacity  of  the  testing  machine. 

47.  From  each  lot  of  rivets  kegged  and  ready  for  shipment  there  shall  be  taken  at 
random  six  (6)  rivets,  to  be  tested  as  follows  : 

(a)  Three  rivets  to  be  flattened  out  cold  under  the  hammer  to  a  thickness  of  one 
half  (^)  the  diameter  of  the  part  flattened,  without  showing  cracks  or  flaws.     Rivets  of 
over  an  inch  in  diameter  shall  be  flattened  to  three  fourths  (|)  of  the  original  diameter. 

(b)  Three  rivets  to  be  flattened  out  hot  under  the  hammer  to  a  thickness  of  at  least 
one  third  (|)  of  the  original  diameter  of  the  part  flattened,  the  heat  to  be  the  ordinary 
driving  heat. 

(c)  From  each  heat  of  rivet  rods  as  finished  at  the  rolls  four  cold-bending  tests  shall 
be  taken,  which  shall  be  bent  over  flat  on  themselves  without  showing  any  cracks  or 
flaws  on  the  outer  round. 

48.  Inspection  for  Surface  and  Other  Defects.  —  Rivets  must  be  true  to  form,  con- 
centric, and  free  from  scale,  fins,  seams,  and  all  other  injurious  or  unsightly  defects. 
Tap  rivets  will  be  milled  under  the  head,  if  necessary  to  obtain  accuracy. 

49.  The  style  of  rivet  used  will  be  determined  by  the  Superintending  Naval  Con- 
structor.    As  a  general  rule,  countersunk  heads  will  be  used  only  where  required  by 
mechanical  or  other  special  reasons.     Wherever  practicable,  the  pan-head  rivet  will  be 
used,  with  countersunk  points  where  flush  work  is  required,  button  or  snap  points  for 
finished  appearance  or  where  rivets  are  closed  by  power  and  hammered  or  mashed 
points  elsewhere.     Where  points  are   made  with  a  snap-tool,  or  where  riveting  by 
power  is  employed,  care  will  be  taken  that  the  points  are  properly  centered.     In  these 
cases,  and  also  in  the  case  of  hammered  points,  the  aim  must  be  to  have  the  point  of 
adequate  strength,  following  as  nearly  as  possible  the  dimensions  of  points  given  in 
Table  LVIII.     Care  must  be  taken  that  snap  points  are  not  reduced  from  the  standard 
sizes  by  grinding  down  tools  that  have  been  chipped  or  burred.      All  pan-head  rivets 
not  less  than  ^  inch  diameter  for  punched  holes  should  be  coned  under  head,  as  shown 
in  Fig.  97,  the  rule  for  punching  from  the  faying  surface  of  plate  being  carefully  ob- 
served.    If,  however,  the  practice  of  punching  the  holes  small  and  reaming  to  size  by 
power  be  employed,  the  coning  under  head  may  be  omitted. 

Proportions  of  Seams. — General  proportions  of  plates,  laps, 
straps,  rivets,  and  spacing  are  given  in  Table  LVII,  page  240. 

Proportions  of  Rivets.  —  The  approved  types  of  head  and  points 
for  torpedo-boats  and  ship  work  are  given  in  Fig.  97,  page  237, 
and  Table  LVIII,  page  241. 


240 


MACHINE   DESIGN. 


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RIVETED   JOINTS. 


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242 


MACHINE    DESIGN. 


The  diameters  of  rivets  and  rivet  holes  for  torpedo-boat  and  ship 
work  are  given  in  : 

TABLE  LIX. 

DIAMETER  OF  RIVETS. 


>v  eigm  01   i  laics. 

V^UI  I  C5  pUUUlIlg 

Rivets. 

i^uircbpuiiumg 
Rivet  Holes. 

FOR  TORPEDO-BOAT  WORK. 

Inches. 

Inches. 

Up  to  3  pounds,  exclusive. 
3  pounds  to  6  pounds,  exclusive. 

\ 

1l 

6  pounds  to  7  5  pounds,  exclusive. 
7i  pounds  to  9  pounds,  exclusive. 
9  pounds  to  1  1  pounds,  exclusive. 

I 

II  pounds  to  13  pounds,  exclusive. 

I 

II 

FOR  SHIP  WORK. 

Up  to  3  pounds,  exclusive. 
3  pounds  to  6  pounds,  exclusive. 
6  pounds,  inclusive,  to  8  pounds,  exclusive. 

1 

1 

8  pounds,  inclusive,  to  13  pounds,  exclusive. 

| 

T5 

13  pounds,  inclusive,  to  20  pounds,  exclusive. 

i 

\\ 

20  pounds,  inclusive,  to  30  pounds,  exclusive. 
30  pounds,  inclusive,  to  40  pounds,  exclusive. 
40  pounds,  inclusive,  to  51  pounds,  exclusive. 

I 

1 

5  1  pounds,  and  above. 

IT 

31 

NOTE. — The  sizes  of  flanges  of  angles  to  which  plates  are  connected  in  torpedo-boat 
work  may  sometimes  be  such  as  to  require  a  reduction  in  the  size  of  the  rivet  to  secure 
satisfactory  workmanship. 

For  connections  between  plates  of  different  thicknesses  and  for 
tap-rivets,  the  requirements  as  to  diameter  are  : 

II.  In  cases  where  rivets  connect  plates  of  different  thicknesses,  the  size  of  rivet 
indicated  for  the  greater  thickness,  with  corresponding  spacing,  will  be  used  where 
strength  is  required,  and  that  indicated  for  the  lesser  thickness  where  water-tightness  is 
a  special  consideration,  always  provided  that  the  greater  thickness  is  not  more  than 
double  the  lesser. 

Where  tap  rivets  must  be  used  they  should  be  \  inch  larger  than  the  corresponding 
ordinary  rivets  for  the  same  thickness,  excepting  taps  into  heavy  forgings  or  castings, 
such  as  stem  and  stern  posts,  which  should  be  \  inch  larger.  Where  strength  is  re- 
quired tap  rivets  must  not  penetrate  less  than  I  diameter,  and  should  penetrate  1 1  diam- 
eters when  the  thickness  of  metal  will  allow  it. 

The  following  extract  and  Table  LX.  refer  to  the  length  of 
rivet  necessary  to  form  the  point : 

19.  Special  care  will  be  taken  in  riveting  that  rivets  used  are  of  sufficient  length  to 
insure  a  proper  point,  the  aim  being  to  have  the  rivet  a  trifle  long,  if  anything.  Such 
cutting  as  is  necessary  should  be  done  while  the  rivet  is  still  a  dull  red,  and  the  point 
finished  after  further  cooling.  Allowances  for  length  over  the  thicknesses  connected 
are  given  in  Table  LX.,  below,  the  allowance  being  for  two  thicknesses  only.  An 
additional  allowance  of  J^  should  be  added  to  that  given  for  each  additional  thickness 
connected,  unless  the  additional  thickness  is  less  than  T3?  inch,  when  gV  inch  additional 
allowance  should  be  sufficient.  The  allowances  given  in  the  table  are  based  upon  the 


RIVETED   JOINTS. 


243 


employment  of  hand  riveting,  and  are  not  sufficient  in  the  case  of  power  riveting,  for 
which  an  added  allowance  —  about  \  inch  —  should  be  made  in  each  case.  This 
table  must  be  used  judiciously  and  not  absolutely  depended  upon. 

TABLE  LX. 
ALLOWANCE  IN  LENGTH  OF  RIVETS  FOR  POINTS. 


In. 

In. 

In. 

In. 

In 

/». 

In. 

Ins. 

Ins. 

Diameter  of  rivet. 

1 

f 

1 

f 

i 

1 

I 

I| 

Ik 

Allowance  for  point,  over  2  thicknesses  connected. 

Type  of  point  : 
Countersunk. 
Hammered. 

t 

I 

\ 

f 

t 

* 

j 

I 

I 

s 

Button. 

\ 

5 

f 

1 

i 

The  allowances  given  above  apply  only  to  rivets  which  fit  the  holes  neatly,  as  here- 
inbefore described. 

Laps  and  Straps.  —  The  required  thickness  of  single  and 
double  butt  straps  is  given  in  the  following  extracts  and  the 
breadth  of  laps  and  straps  in  Table  LXI. 

TABLE  LXI. 

BREADTH  OF  LAPS  AND  STRAPS. 


Diameters. 

Breadth  of  laps  for  single  riveting. 
Breadth  of  laps  for  double  chain  riveting. 
Breadth  of  laps  for  double  zigzag  riveting. 
Breadth  of  double-riveted  butt  laps. 
Breadth  of  laps  for  treble  riveting. 
Breadth  of  treble-riveted  butt  laps  in  outside  plating. 
Breadth  of  edge  strip  for  single  riveting. 
Breadth  of  edge  strip  for  double  riveting. 
Breadth  of  butt  strap  for  double  riveting. 
Breadth  of  butt  strap  for  treble  riveting. 
Breadth  of  double  butt  strap,  double-riveted. 
Breadth  of  double  butt  strap,  treble-riveted. 

5; 

5 

8 
9 
6 
Hi 
Hi 
16 

12 

\ 

SINGLE  STRAPS. 

1 6.  Single  butt  straps  and  edge  strips,  when  single-  or  double-riveted,  should  be  of 
the  same  thickness  as  the  plates  connected,  and  where  the  plates  connected  are  of 
different  thickness  they  should  be  of  the  same  thickness  as  the  lighter  plate.     Single 
butt  straps,  when   treble-riveted,  should  be  i^  times  the  thickness  of  plates  which 
they  connect. 

DOUBLE  BUTT  STRAPS. 

17.  Double  butt  straps  should  not  be  used  for  water-tight  work,  owing  to  difficulty 
in  calking.     They  may  be  used  to  advantage,  however,  in  connections  requiring  great 
strength,  but  not  water-tightness.     The  thickness  of  each  strap  should  be  one  half  the 


244 


MACHINE    DESIGN. 


thickness  of  plates  connected  for  double-riveted  straps  and  five  eighths  the  thickness  for 
treble-riveted  straps.  *  *  *  For  double  butt  straps  the  size  of  rivet  to  be  used 
should  be  as  follows  : 

For  plates  from  15  to  20  pounds,  exclusive,  f-inch  rivets. 

For  plates  from  20  to  25  pounds,  inclusive,  f -inch  rivets. 

For  plates  above  25  pounds,  as  per  Table  LIX. 

Since  double  butt  straps  are,  as  a  rule,  used  in  hull  work  in 
joints  requiring  strength  but  not  tightness,  the  spacing  of  the  rivets 
in  such  joints  is  that  required  for  maximum  efficiency,  the  assump- 
tions being :  Tensile  strength  of  plate,  63,000  Ibs.  per  sq.  in.; 
shearing  strength  of  rivets,  50,000  Ibs.  per  sq.  in. ;  for  single 
straps,  plate  to  be  through-countersunk. 

TABLE  LXII. 
SPACING  OF  RIVETS. 


Number  of 
;   Diameters  from 
Center  to  Center. 


Single-riveted  laps  and  straps. 

Double-riveted  laps  and  straps. 

Treble-riveted  laps. 

Treble-riveted  straps,  with  alternate  rivets  in  third  row  omitted. 

Longitudinal  seams  of  plating  required  to  be  water-tight  (excepting 
single-riveted  laps  and  straps). 

Connections  of  transverse  frames  not  water-tight  to  outside  plating. 

Connections  of  deck  plating  to  beams  ;  of  nonwater-tight  longitudinals 
to  outside  plating ;  of  the  angles  and  stiffeners  to  bulkheads  when  ' 
entirely  above  the  water  line,  and  in  general  where  special  strength 
is  not  required. 

Connections  of  floor  plates,  brackets,  lightened  intercostals,  etc.,  to 
clips  and  angles  ;  of  the  vertical  keel  angles  to  the  flat  and  vertical 
keel  plates  and  to  the  flat  keelson  plates  beyond  the  limits  of  double 
bottom,  provided  water-tightness  is  not  required. 

Connections  of  angles  and  other  stiffeners  to  bulkheads  at  or  below  the 
water  line  ;  of  boiler  and  engine  bearings  and  foundations  generally. 

Connections  of  inner  bottom  plating  to  all  frames  and  longitudinals. 

Connections  of  angles  of  water-tight  frames  and  longitudinals  to  all 
plating,  and  in  general  where  water-tightness  is  required  between 
shapes  and  plates. 

Angles  and  other  stiffeners  to  bulkheads  forming  supports  to  turrets, 
barbettes,  connections  of  armor  shelf  angles  to  plating,  etc. 

Connections  between  staple  angles  of  water-tight  floors  and  the  floor 
plates. 

In  special  cases  of  intercostals,  beam  ends,  etc.,  where  strength  is  re- 
quired in  connections  of  limited  extent,  and  in  all  other  exceptional 
cases,  spacing  to  be  as  required  by  circumstances,  except  that  the 
rivets  in  the  same  line  should  never  be  spaced  less  than 


Rivet-spacing.  —  General  proportions  for  the  spacing  of  rivets 
are  given  in  Table  LXII.  Where  this  spacing  cannot  be  followed 
exactly,  it  may  be  slightly  closer  for  heavy  plates  and  slightly 


RIVETED   JOINTS.  245 

wider  for  light  plates.  The  division  between  "  light "  and  "  heavy  " 
plates  lies,  with  single-riveting,  at  7^-lb.  plates ;  with  double- 
riveting  at  15-lb.  plates;  and,  with  treble-riveting  at  25-lb.  plates. 

15.  When  strength  is  required  in  laps  and  butted  connections  of  plating,  with  the 
spacing  indicated,  single-riveting  is  suitable  only  for  plating  under  12^  pounds  and 
double-riveting  for  plating  under  25  pounds.  *  *  *  For  maximum  strength  in  connec- 
tions of  plating  above  30  pounds  it  will  generally  be  found  that  quadruple-riveting  is  re- 
quired. 

DISTANCE  BETWEEN  Rows. 

1 8.  Centers  of  rivets  should  be  placed  not  less  than  if  times  the  diameter  from  the 
edges  of  plates  connected.  In  double-  and  treble-riveting,  for  laps  and  single  straps,  the 
distance  from  centre  to  centre  of  rows  should  not  be  less  than  z\  diameters  ;  in  butt  laps  and 
double  butt  straps  the  distance  between  centres  of  rows  should  be  not  less  than  3  di- 
ameters (butt  laps  should  be  at  least  double-riveted).  For  zigzag  riveting  the  distance 
between  centres  of  rows  should  not  be  less  than  i|  diameters  for  rivets  spaced  4  di- 
ameters apart  in  rows. 

Punching,  Drilling,  Riveting. — The  size  of  the  rivet-hole  for  a 
given  diameter  of  rivet  has  been  given  previously. 

4.  All  rivet  holes  through  material  i  inch  or  more  in  thickness  should  be  drilled,  or, 
if  punched,  should  afterwards  be  reamed  to  finished  size.     The  increase  in  diameter  of 
hole  due  to  reaming  should  be  equal  to  at  least  one  eighth  the  thickness  of  the  material. 
In  punching,  where  possible,  holes  will  be  punched  from  the  side  which  will  form  the 
faying  surface. 

5.  Great  care  must  be  taken  in  punching  to  prevent  holes  from  coming  unfair.    Any 
unfair  hole  must  be  reamed  out  before  riveting,  and  a  rivet  suitable  to  the  increased  size 
of  hole  inserted. 

In  countersunk  holes,  where  the  depth,  B,  given  in  Fig.  97, 
would  extend  through  the  plate,  the  countersink  should  be  carried 
to  within  ^  in.  of  the  bottom.  Power  riveting  is  preferred  for 
torpedo-boat  work.  Rivets,  in  general,  less  than  |-in.  diameter 
should  be  driven  cold ;  in  torpedo-boat  work,  j^-in.  rivets  also 
may  be  thus  driven. 

2.  AMERICAN  BUREAU  OF  SHIPPING.  —  In  the  rules  of  this 
bureau  for  the  building  and  classing  of  vessels,  the  character  as- 
signed to  the  latter  is  expressed  by  numerals  ranging  from  A  i  to 
A  3,  the  former  being  the  highest  grade  and  corresponding  with 
the  grades  A  i  of  Lloyd's  Register  and  3/3  —  i.i  of  the  Bureau 
Veritas.  Vessels  classified  under  the  latter  grades  are  regarded 
as  fitted  for  the  carriage  of  all  kinds  of  cargo  on  all  voyages. 
New  vessels  built  in  conformity  with,  or  equal  to,  the  rules  of  the 
American  Bureau  are  graded  thus  :  1st  Class,  A  i  for  17  years  ; 
2d  Class,  A  i  for  13  years  ;  3d  Class,  A  i  for  10  years.  If  built 
under  inspection,  these  terms  are  increased  by  three  years  for  the 


246 


MACHINE   DESIGN. 


1st  and  2d  classes  and  by  two  years  for  all  others.     The  follow- 
ing extracts  are  taken  from  the  rules  (1901)  of  this  Bureau  : 

Outside  {skin)  Plating :  of  all  (steel)  steam  vessels  whose  length  does  not  exceed 
TI  times  their  depth  to  be,  for  half  the  vessel's  length  amidships,  and  at  ends,  the  thick- 
ness specified  in  Table  LXIII.  *  *  *  Skin  plates  (in  general)  must  not  be  less  than 
6  frame  spaces  in  length.  *  *  *  Butts  in  adjoining  strakes  must  be  shifted  clear  of  each 
other  not  less  than  two  frame-spaces.  Butts  in  alternate  strakes  must  have  a  clear  shift 
of  not  less  than  one  frame-space.  *  *  *  The  butts  of  all  skin-plates  must  be  planed  and 
close  fitted  and  the  butt-straps  be  drawn  up  iron  to  iron.  *  *  *  The  edges  of  all  skin 
plates  to  be  sheared  from  their  faying  surfaces  and  those  of  outside  strakes  to  be  planed 
or  chipped  fair.  All  butts  and  seams  to  be  efficiently  calked.  *  *  *  The  skin  plat- 
ing can  be  worked  in  out-and-in  strakes  or  flush.  If  worked  in  out-and-in  strakes,  the 
insides  strakes  must  be  fitted  to  frames,  iron  to  iron,  and  solid  liners  must  be  fitted  be- 
tween the  frames  and  the  outside  strakes.  *  *  *  If  the  skin  plating  is  worked  flush, 
*  *  *  continuous  edge-strips,  with  their  butts  shifted  well  clear  of  the  butts  of  the  skin- 
plating  to  which  they  are  secured,  must  be  properly  worked  on  the  plating  seams. 


TABLE*  LXIII. 
MINIMUM  THICKNESS  OF  OUTSIDE  PLATING  AND  FLAT  PLATE  KEEL. 


17  Years  Class.     Thickness  in  Lbs.,  Per  Square  Foot. 

Sheer 
Strake. 

Sheer  to 
Bilge. 

Bilge  and 
Bottom. 

Garboards. 

Flat  Plate 
Keel. 

Numerals.! 

,c    . 

.e    . 

wC        . 

j3     . 

j-       . 

If 

Si 

1 

It 

1 

j 

II 

If 

i 

~5  B 

rt  c 

P 

w 

!s| 

|| 

2,000  and  under      3,500 

12 

10 

IO 

9 

II 

10 

12 

12 

16 

12 

5,000                      6,500 

16 

14 

13 

II 

14 

12 

16 

l,S 

18 

14 

8,000                     10,000 

19 

16 

15 

12 

16 

13 

18 

16 

22 

18 

14,000                     16,500 

24 

19 

17 

14 

19 

16 

21 

19 

28 

22 

I9,OOO                               22,000 
30,000                              36,000 

27 
2Q 

20 
22 

19 
22 

15 

18 

21 
24 

17 

20 

11 

21 
24 

32 

24 
27 

42,000                              48,000 

24 

24 

19 

26 

21 

28 

2S 

37 

28 

56,000                              64,000 

31 

26 

21 

28 

22 

30 

27 

39 

29 

72,000                               80,000 

26 

28 

22 

30 

24 

32 

29 

31 

IOO,OOO                            IIO,OOO 

3<> 

27 

30 

24 

33 

26    j  35 

30 

44 

32 

NOTE. — The  following  to  be  the  minimum  width  of  main  sheer  strake  for  f  length 
amidships  for  vessels  of  all  grades.  Numeral  under  10,000,  33  inches  ;  numeral  10,000 
and  under  16,500,  36  inches  ;  numeral  16,500  and  under  22,000,  40  inches  ;  numeral 
22,000  and  above,  45  inches. 

The  minimum  width  of  garboards  and  flat-plate  keels  for  f  length  amidships  for 
vessels  of  all  grades  to  be  as  follows  :  numeral  under  10,000,  30  inches  ;  numeral  10,000 
and  under  16,500,  33  inches  ;  numeral  16,500  and  above,  36  inches. 

*The  table  is  reproduced  in  part  and  for  the  17-year  class  only. 

fThe  numeral  =  (Depth  -f-  £  breadth  -f  |  girth)  in  ft.  X  length,  in  ft. 


RIVETED   JOINTS. 


24? 


Butt-straps  : 

The  widths  for  single-,  double-,  and  treble-riveted  butt-straps,  suited  to  different 
series  of  rivets,  are  specified  in  Table  LXIV.  *  *  *  Butt  straps  must  in  no  case  be 
less  than  2  Ibs.  thicker  than  the  plates  to  which  they  are  secured.  Treble-riveted  butt 
straps  must,  in  all  cases,  be  at  least  4  Ibs.  thicker  than  the  plates  to  which  they  are 
secured. 


TABLE  LXIV. 

FOR  DIAMETER  OF  RIVETS,  BREADTH  OF  LAPS,  LAPPED  BUTTS,  WIDTH  OF 
BUTT  STRAPS  AND  BREADTH  OF  EDGE  STRIPS  ON  PLATE  SEAMS. 


Thickness  of  Plates  in  Ibs.  weight 

1 

per  square  foot. 
Diameter  of  Rivets  in  sixteenths 

IO 

"1 

15 

*7i 

20 

221 

*5 

27; 

30 

321 

35 

37* 

40 

of  an  inch. 

9 

IO 

ii 

12 

12 

12 

14 

14 

16 

16 

18 

iS 

20 

Size  in  inches  of  Countersink  for 

Rivets  of  Plating. 
Breadth  of  Laps,  in  inches,   for 

I 

I 

iA 

*A 

'A 

'A 

iA 

'A 

iA 

'A 

i« 

Iff 

i« 

Single  Riveting. 

2 

at 

*1 

2f 

H 

2f 

Breadth  of  Laps,  in  inches,  for 

Double  Riveting. 
Width  of  Butt  Straps,  in  inches, 

31 

3* 

4 

41 

41 

41 

5i 

5k 

6 

6 

7 

7 

71 

Double  Riveted. 
Width  of  Butt  Straps,  in  inches, 

7 

7* 

81 

91 

91 

91 

ii 

ii 

"1 

1*1 

14 

14 

'5i 

Treble  Riveted. 
Breadth  of  Edge  Strips  for  Plate 

IOJ 

"1 

I2f 

14 

14 

14 

i6i 

i6J 

18* 

iSi 

21 

21 

23 

Seams,    in   inches,  for   Single 

Riveting. 
Breadth  of  Edge  Strips  for  Plate 

4 

41 

4f 

51 

51 

51 

6i 

6* 

71 

71 

81 

81 

9 

Seams,  in  inches,  for  Double 

Riveting. 
Breadth  of  Double-riveted  Butt 

71 

8 

8* 

9:! 

9t 

9f 

ii 

ii 

13 

13 

141 

Ul 

15? 

Laps. 

41 

4i 

5 

5 

5 

6 

6 

6 

6 

6 

Breadth  of  Treble-riveted  Butt 

Laps. 

71 

7j 

9 

9 

9 

9 

roj 

roi 

wj 

The  number  and  thickness  of  butt-straps  varies  with  the  ves- 
sel's numeral  for  plating.  The  following  specification  applies  to 
the  hull  whose  midship  section  is  shown  in  Fig.  98. 

Vessels  whose  numeral  is  30,000  and  under  48,000  to  have  the  butts  of  sheer 
strake,  2  strakes  of  plating  at  bilge  and  upper  deck  stringer-plate  secured  with  treble- 
riveted  butt  straps  for  J  the  vessel's  length  amidships.  The  butt  straps  of  bilge  and  shear- 
strakes,  also  deck  stringer-plate  if  it  is  under  54  ins.  wide,  to  be  7  Ibs.  thicker  than  the 
plate  to  which  they  are  secured.  The  back  row  of  rivets  in  foregoing  butt  straps  to  be 
spaced  similar  to  the  other  rows.  In  addition  to  above,  the  remaining  skin-plates  are 
to  be  secured  at  their  butts  with  treble-riveted  butt  straps  7  Ibs.  thicker  than  the  plates 
to  which  they  are  secured  for  |  the  vessel's  length  amidships.  If  any  of  the  foregoing 
skin  plates  exceeds  54  ins.  in  width,  the  butts  of  same  are  to  have  butt  straps  IO  Ibs. 
thicker  than  the  plates  to  which  they  are  secured.  *  *  *  When  the  vessel's  numeral 
is,  or  exceeds,  16,500,  the  lapped  butts  of  outside  plating  are  to  be  treble-riveted 
throughout. 


248  MACHINE   DESIGN. 

Rivets  and  Rivet-  Work  : 

I.  The  diameters  of  rivets  for  the  different  thicknesses  of  plates  and  angle  bars  are 
specified  in  Table  LXIV.  2.  The  longitudinal  laps  of  skin  plating,  except  main  sheer 
strake,  worked  in,  out-  and  in-strakes,  and  which  is  sixteen  pounds  and  above  in  thick- 
ness, to  be  double-riveted.  Main  sheer  strakes  fourteen  pounds  and  above  to  have  the 
lap  at  their  lower  edge  double-riveted.  3.  The  longitudinal  seams  of  skin  plating  that 
is  worked  flush,  and  which  is  twenty  pounds  and  above  in  thickness,  to  be  secured 
with  edge  strips  having  two  rows  of  rivets  on  each  side  of  seam.  4.  The  longitudinal 
laps  of  skin-plating  which  is  under  the  above  specified  thicknesses,  for  double-riveting, 
to  be  single-riveted.  5.  All  double-riveting  in  longitudinal  laps  and  edges  to  be  chain 
fashion,  the  distance  between  the  rows  in  lap  riveting  to  be  not  less  than  two  and  three 
quarter  times,  nor  more  than  three  times  the  diameter  of  rivet,  from  centre  to  centre  of 
rivet  and  the  laps  are  to  be  not  less  in  width  than  six  times  the  diameter  of  rivet. 
Double  riveted  edge  strips  to  be  the  width  specified  in  Table  LXIV.,  and  the  spacing  of 
rivets  between  rows  to  be  similar  to  that  hereafter  specified  for  double-riveted  butt 
straps.  6.  Single-riveted  laps  to  be,  in  width,  three  and  a  half  times  the  diameter  of 
rivet.  Single-riveted  edge  strips  to  be  the  width  specified  in  Table  LXIV.  7. 
Longitudinally  the  distance  between  rivets  in  laps  and  edges,  of  skin  plating,  and 
the  laps  and  seams  of  all  plating  required  to  be  calked  watertight,  to  be,  from 
centre  to  centre,  four  times  the  diameter  of  rivet,  providing  the  plating  does  not  exceed 
twenty  pounds  in  thickness  ;  if  the  plating  exceeds  twenty  pounds  in  thickness,  the  dis- 
tance may  be  four  and  a  half  times  the  diameter  of  rivet.  8.  The  rivets  in  all  butts  — 
except  the  third  row  of  a  butt  which  is  treble-riveted  —  are  to  be  spaced  apart,  from 
centre  to  centre,  three  and  a  half  times  the  diameter  of  rivet ;  and  the  distance  between 
rows  of  butt  rivets  to  be  from  two  and  a  half  to  three  diameters  of  rivet,  from  centre  to 
centre  of  row.  9.  The  rivets  in  the  third  row  of  a  butt,  which  is  treble-riveted,  may  be 
seven  diameters  of  rivets  apart,  from  centre  to  centre,  except  otherwise  specified.  10. 
The  spacing  of  the  rivets  which  secure  the  frames  to  skin  plating,  and  to  floor  plates,  to 
be,  from  centre  to  centre,  not  more  than  seven  and  a  half  times  the  diameter  of  rivet, 
except  frames  having  watertight  bulkheads  secured  to  them,  in  which  the  spacing,  from 
centre  to  centre,  must  not  exceed  five  times  the  diameter  of  rivet.  *  *  *  15.  When  the 
thickness  of  skin-plating  amidships  demands  double-riveted  laps  or  edges,  the  same  is 
to  be  continued  right  fore  and  aft.  16.  The  diameter  of  rivets  for  securing  plates,  or 
plates  and  angle  bars,  of  different  thicknesses,  to  each  other  to  be  regulated  by  the 
thicker  of  the  two.  17.  When  three  or  more  thicknesses  are  riveted  together,  the 
thickest  of  the  parts  is  to  regulate  the  diameter  of  rivet.  *  *  *  20.  Rivet  holes  are  to 
be  fairly  and  regularly  pitched,  and  must  in  no  case  be  nearer  the  edge  of  a  plate  or 
angle  bar  than  their  diameter.  21.  It  is  recommended  that  all  rivet  holes  be  punched 
one  sixteenth  of  an  inch  smaller  than  the  diameter  of  rivet  to  be  used,  and  the  holes  be 
reamed  to  the  size  of  rivet  after  the  parts  are  in  place.  Any  structure,  or  parts,  where 
more  than  two  thicknesses  of  material  are  riveted  together,  and  all  longitudinals,  floors 
or  brackets  in  double  bottom,  also  keelsons  and  stringers  in  holds,  to  have  their  rivet 
holes  punched  one  sixteenth  less  than  the  size  of  rivet  to  be  used,  and  the  holes  reamed 
to  size  of  rivet  after  the  parts  are  in  place.  22.  Rivet  holes  are  to  be  punched  from 
the  faying  surfaces  of  the  different  parts,  and  great  care  must  be  taken  to  have  them, 
in  the  different  parts  joined,  truly  opposite  each  other.  When  holes,  in  the  parts  joined, 
are  not  truly  opposite  each  other,  heavy  drifting  must  not  be  resorted  to  ;  the  holes 
must  be  reamed  or  drilled  fair  and  a  larger  size  rivet  used.  23.  The  rivet  holes  in 
frames  opposite  skin-plate  laps  or  edges  to  be  drilled  after  the  plates  are  fitted  in  place. 
*  *  *  25.  Rivets  in  skin  plating  *  *  *  to  have  their  necks  beveled  under  the  rivet- 
heads  so  as  to  fill  the  countersink  made  in  punching.  26.  Rivet-heads  should  not  be 
thicker  than  f  the  diameter  of  rivet.  The  countersinking  of  all  plates  and  angle-bars 


RIVETED   JOINTS. 


249 


to  be  made  by  drill  and  the  countersink  to  extend  right  tnrough  the  piate  or  angle-bar 
27.  Each  rivet  to  fill  its  hole,  the  heads  of  those  for  skin  plating  to  be  close  laid  up  and 
the  rivets  outside  finished  flush  and  fair,  except  in  keel,  stem,  and  stern-post,  where 
they  must  be  slightly  convex. 


Fig.  98  is  a  midship  section  of  a  typical  steel,  3 -deck,  screw 
steamer  of  the  17-year  class.  The  principal  data  are:  Length, 
415  ft.  ;  breadth,  48  ft.  ;  depth,  32  ft. ;  J  girth  to  second  deck, 
43.5  ft.  ;  |  breadth  moulded,  24  ft.  ;  depth  to  upper  deck,  32  ft. ; 
numeral  for  outside  plating  =  (43.5  -f  24  +  32)415  =  41,292. 

Longitudinal  Seams. 

a.  Lap,  6  in.  wide,  i  in.  rivets ; 

b.  Lap,  5  J  in.  wide,  J  in.  rivets ; 

c.  Lap,  4-J  in.  wide,  f  in.  rivets. 


250 


MACHINE   DESIGN. 


PLATING  AND  TRANSVERSE  SEAMS. 


Plating. 

Thickness  in  Ibs.  per  sq.  ft. 

Seam. 

|I-g«-d. 

At  ends. 

Throughout. 

Treble-riveted  butt  for. 

A.   Bulwarks. 

10 

B.  Sheer  strake. 

33 

23 

J  length. 

C 

D. 

25 
23 

18 
18 

f  length  amidships, 
f  length  amidships. 

E. 

30 

20 

\  length  amidships. 

F. 

28 

20 

|  length  amidships. 

G. 

23 

20 

f  length  amidships. 

H.  Garboards. 

25 

f  length  amidships. 

K.  Keel,  outer  plate. 
Keel,  inner  plate. 

34 
25 

28 

extends  \  ICE 

gth  amid. 

Throughout. 
Throughout. 

CHAPTER   V. 

KEYED   JOINTS;    PIN-JOINTS. 

The  term  "key"  is  applied  to  two  forms  of  removable  fasten- 
ings :  The  key  proper,  which  is  splined  in  a  shaft  to  prevent  relative 
rotation  and  sometimes  axial  movement  of  an  attached  member, 
as  a  pulley  or  gear-wheel ;  and  the  "through-key"  or  "  cotter" 
which  joins  parts  subjected  to  tensile  or  compressive  stress  or  to 
both,  as  the  sections  of  a  pump-rod,  the  strap  and  body  of  a  con- 
necting rod,  etc.  The  key  proper  is  purely  a  locking  device  de- 
signed to  resist  shearing  stress  on  the  sectional  area  formed  by  its 
breadth  and  length  ;  the  cotter  not  only  unites  the  parts,  but,  if 
of  suitable  length,  gives,  through  its  taper,  a  limited  range  of  axial 
adjustment,  while  it  withstands  shearing  at  two  transverse  sections, 
each  the  product  of  its  breadth  and  depth.  Both  forms  are  made 
generally  of  steel,  although  wrought  iron  finds  infrequent  use. 

54.     Forms  of  Keys. 

Keys  for  shafting  may  be  classified  as  :  Sunk  keys,  i.  e.,  those 
which  are  fitted  in  key-seats  cut  in  the  shaft  and  in  the  attached 
hub  ;  Friction  keys,  for  which  the  key-seat  in  the  shaft  is  omitted 
and  which  drive,  or  are  driven  by,  the  latter  through  friction  only  ; 
and  Keys  on  the  Flat  which,  in  their  action,  are  intermediate 
between  the  two  former  classes. 

i .  SUNK  KEYS  are  almost  universally  of  the  square  or  flat  forms, 
shown  in  Figs.  99  and  100,  respectively. 

Square  Keys  prevent  relative  rota- 
tion  only.  They  are  approximately 
square  in  section  with  opposite  sides 
parallel  ;  the  width,  W,  is  slightly 
less  than  the  depth,  T,  and  the  key 
is  sunk  in  the  shaft  a  little  more 
than  1  T;  the  key  bears  only  on 
the  sides  of  the  key-seats  in  shaft 

and  hub,  there  being  usually  a  slight  clearance  at  top  and  bot- 
tom. Such  a  key  will  not  secure  the  attached  hub  against  axial 
movement.  The  latter  must  be  prevented  by  set-screws  pass- 

251 


252  MACHINE   DESIGN. 

ing  through  the  hub  and  bearing  on  the  key  ;  by  making  the 
hub  a  shrinkage  or  forced  fit  on  the  shaft ;  by  splitting  the 
hub,  boring  it  for  a  pressure  fit,  and  drawing  the  split  to- 
gether with  bolts ;  by  using  loose  collars  with  set-screws  on  the 
shaft  at  the  ends  of  the  hub  ;  or,  finally,  if  the  hub  be  keyed  at 
the  extremity  of  the  shaft,  by  threading  a  nut  on  the  latter.  On 
the  other  hand,  the  square  key  drives  practically  through  its  resist- 
ance to  shearing  stress  on  a  longitudinal  section,  and,  therefore, 
exerts  no  bursting  pressure  upon  the  hub  and  has  no  tendency  to 
force  the  latter  into  eccentricity  with  the  shaft.  Hence,  while  its 
liability  to  tipping  in  its  seat  unfits  it  —  unless  secured  by  screws 
or  dowels  —  for  heavy  loads,  it  is  suitable  for  machine  tools  or 
other  work  in  which  accurate  concentricity  is  required  or  in  which 
the  parts  may  be  disconnected  frequently. 

The  Flat  Key  (Fig.  100)  locks  both  axially  and  circumferen- 
tially.  Its  section  is  rectangular  and  its  sides  are  parallel,  but 
its  top  and  bottom,  while  plane,  are 
inclined  toward  each  other  to  form  a 
wedge.  The  key  is  fitted  accurately 
on  all  four  surfaces.  When  driven 
home,  the  compression  and  elasticity 

of  its  metal  and  that  of  the  hub,  lock 
FIG.  100.  ,  . .  . 

the  latter  effectually  against  motion  in 

any  direction.  There  are,  however,  a  bursting  pressure  upon  the  hub 
and  a  tendency  to  spring  the  latter  out  of  truth,  both  with  the  axis 
and  with  a  plane  normal  to  it.  This  key,  as  Mr.  John  Richards  has 
pointed  out,  drives  as  a  diagonal  strut  rather  than  by  pressure 
normal  to  its  face.  If  the  angle,  a,  Fig.  100,  be  made  about  30°, 
fair  proportions  will  be  obtained  with  a  reasonably  low  value  for 
the  magnitude  of  the  bursting  element  of  the  driving  force.  The 
taper  is  usually  ^-inch  per  foot.  The  key  is  suitable  for  heavy 
or  light  work  in  which  slight  inaccuracy  in  adjustment  is  not 
material. 

The  Feather  Key  is  a  square  key  fitted  for  relative  axial  move- 
ment of  the  connected  parts,  as  in  a  clutch-coupling.  The  key  is 
secured  in  a  key-seat  in  either  the  shaft  or  hub  and  the  other  key- 
way  is  made  a  working  fit.  The  necessary  surface  to  prevent  wear 
from  sliding  movement  may  be  had  by  increasing  the  length  and  to 
some  extent  the  depth  of  the  key.  The  latter  is  fastened  to  the  seat 
either  by  countersunk  screws,  or  by  dove-tailed  ends,  or,  in  the  case 


KEYED   JOINTS;    PIN-JOINTS. 


253 


FIG.  101. 


of  a  hub,  by  gib  (hooked)  heads  at  the  extremities  of  the  feather. 
When  the  required  surface  warrants  their  use,  two  feather-keys 
set  diametrically  apart  are  better  than  one  in  equalizing  the  strain. 
The  Woodruff  Key  *  (Fig.  101)  may  be  of  either  the  "  square  "  or 
"  flat  "  types.  It  has  one-milled  key-seat  with  parallel  sides,  but 
of  circular  outline  at  the  bottom  and  hence 
of  varying  depth  ;  the  other  key-seat  is  of 
the  usual  form.  The  maximum  depth  of 
the  circular  key -seat  is  considerably  greater 
than  that  of  the  ordinary  type  and  the 
shaft  is,  at  that  point,  correspondingly 
weaker.  On  the  other  hand,  the  key  is  so 
firmly  inset  that  it  cannot  possibly  tip  in 
its  seat  as  the  usual  key  may  ;  and,  further, 
the  circular  key  will  rotate  in  its  seat  until  accurate  adjustment 
with  an  angular  spline  is  obtained,  while  the  ordinary  taper  key 
may  bear  at  one  point  only,  if  not  well  fitted.  In  order  to  avoid 
cutting  too  deeply  into  the  shaft  in  securing  a  long  hub,  two  or 
more  "  square  "  Woodruff  keys  may  be  inset  in  axial  alignment 
with  each  other  so  as  to  engage  the  same  key-seat  in  the  hub. 

"Quartering"  Keys.  —  With  large  shafts,  especially  when  the 
hub  to  be  secured  is  a  loose  fit,  it  is  better  to  use  two  keys  set  90° 
apart  on  the  shaft,  since  the  second  key  will  oppose  the  hub's 
tendency  to  rock  on  the  single  key  as  a  pivot.  If  two  sunk  keys 
be  thus  used,  the  width,  W,  of  each  need  be  but  one  half  that 
required  for  a  single  key  while  the  thickness,  T,  will  also  be  less. 
In  some  cases,  a  sunk  key  is  used  to 
do  the  driving  while  a  saddle-key  or  key 
on  the  flat,  set  quartering,  steadies  the 
hub  and  gives  a  rigid  joint. 

The  Peters  System  of  semi-sunk  keys 
is  shown  in  Fig.  102.  It  is  suitable  es- 
pecially for  fastening  members  having  a 
reciprocating  motion,  either  rotary  or 
rectilinear,  as,  for  example,  a  rock-shaft 
arm.  There  are  two  pairs  of  keys  set 
The  keys  of  each  pair  have  each  one 
The  latter  engage,  while  the  parallel 


FIG.  102. 


preferably    135°  apart, 
parallel  and  one  tapered  side. 


*  The  Whitney  Manufacturing  Co. ,  Hartford,  Conn. 


\ 


254 


MACHINE   DESIGN. 


FIG.  103. 


sides  abut  against  those  of  parallel-sided  key-seats.     The  seats  are 
normal  to  a  radial  and  are  partly  in  both  shaft  and  hub,  so  that,  for 
motion  in  either  direction,  the  system  supplies  a  radial  driving  face. 
The  tapered  sides    enable   the   keys,  when  driven 
home,  to  make  a  rigid  joint. 

Pin-Keys,  Fig.  103,  may  be  used  when  the  hub 
to  be  secured  is  on  the  end  of  the  shaft.  A  cylin- 
drical or  taper  hole  is  drilled  and  reamed  at  the 
shaft  circumference,  parallel  to  the  axis,  and  one 
half  each  in  shaft  and  hub.  Into  this  hole  a  closely 
fitting  cylindrical  or  taper-pin  is  driven  which  thus  forms  a  sunk 
key.  The  method  is  accurate  and  cheap  but  is  used  only  with 
light  work. 

2.   FRICTION  KEYS. — With  this  form  no  key-seat  is  cut  in  the 
shaft,  the  holding  power  of  the  key  being  due  to  friction  only. 

The  Saddle  Key  is  shown  in  Fig.  1 04. 
The  sides  are  parallel,  the  top  tapered, 
and  the  bottom  concave,  to  fit  the  shaft. 
When  the  key  is  driven  home,  the  friction 
causes  it  to  grip  the  shaft.  Its  driving 
power  is  small  and  the  principal  uses  of 
the  key  are  to  prevent  rocking,  when 
set  quartering  with  a  sunk  key,  and  in 

temporary  service,  as  in  setting  an  eccentric.     Locomotive  eccen- 
trics are  sometimes  secured  permanently  by  two  saddle-keys,  fitted 

90°  apart,  whose  curved  faces  have 
longitudinal  grooves  or  teeth  which 
cut  into  the  shaft  when  the  keys 
are  driven  home. 

The  Kernatil  Key*  Fig.  105, 
drives  only  in  one  direction.  The 
key,  K,  is  approximately  a  seg- 
ment somewhat  less  than  90°  in 
extent,  the  inner  face  of  which  is 
curved  to  the  radius  of  the  shaft, 
the  outer  to  that  of  an  eccentric 
slot,  S,  formed  in  the  hub,  H. 

The  inner  surface  of  the  key  is  left  rough,  the  outer  being  finished 
and  smooth.     Hence,  when  the  hub  is  rotated  in  the  direction  of 


FIG.  104. 


FIG.  105. 


*Reuleaux's  "Constructor,"  Suplee  translation,  1895,  p.  49. 


KEYED   JOINTS;    PIN-JOINTS.  255 

the  arrow,  it  slides  over  the  key  until  the  latter  grips  and  revolves 
the  shaft.  A  set-screw  at  a  is  used  to  set  up  the  key  and  a  simi- 
lar one  at  b  to  loosen  it. 

The  Blanton  Fastening*  while  not  a  friction-key,  is,  to  some 
extent,  a  modification  of  the  Kernaul  principle.  If,  in  Fig.  105, 
the  key,  K,  be  fixed  on  the  shaft,  it  is  evident  that,  with  the  circum- 
ferential clearance  shown  in  the  slot,  S,  the  hub,  H,  will  drive  the 
shaft  when  rotated  in  the  direction  of  the  arrow ;  but,  when  the 
direction  of  rotation  is  reversed,  the  hub  will  become  loose  with 
limited  angular  play,  so  that  it  may  be  slipped  along  the  shaft  and 
removed  readily.  This  is  essentially  the  principle  of  the  Blanton 
fastening  which  is  applicable  especially  to  the  lifting  cams  of  ore 
stamp-mills,  largely  because  of  the  ease  with  which  the  cams  may 
be  disconnected  and  others  substituted.  The  surface  of  the  shaft 
is  formed  in  a  series  of  corrugations  corresponding  with  a  series  of 
keys,  K,  and  the  hub  is  slotted  to  fit,  with  clearance  at  the  ends 
of  the  slots,  which  ends  are  inclined  and  not  radial,  as  in  Fig.  105. 

Roller  Keys.  —  If,  in  Fig.  105,  there  be  substituted  for  the  key 
a  hardened  steel  cylindrical  roller  whose  diameter  is  a  little  less 
than  the  maximum  radial  width  of  the  slot,  S,  it  is  obvious  that 
a  slight  rotation  of  the  hub  will  cause  the  roller  to  bind  and  thus 
drive  the  shaft.  The  connection  is,  like  the  Blanton,  readily  dis- 
engaged but  is  suitable  for  light  work  only.  In  fitting  it,  the  ends 
of  the  hub  are  bored  concentrically  with  the  shaft  and  to  the  diam- 
eter of  the  latter,  while  the  central  recess  for  the  key  is  circular 
but  eccentric  with  the  shaft. 

The  Cone-Key  depends  wholly  upon  friction  for  its  driving  power. 
The  hub  of  the  pulley  or  other  member  to  be  secured,  is  bored 
centrally  with  a  tapered  hole  whose  least  diameter  is  greater  than 
that  of  the  shaft.  A  cast-iron  bushing,  bored  to  fit  the  shaft  and 
turned  to  the  taper  of  the  hub-bore,  is  then  split  longitudinally 
into  three  equal  parts,  giving  thus  three  saddle-keys,  each  nearly 
120°  long  circumferentially.  These  keys,  forced  between  shaft 
and  hub,  hold  and  drive  the  latter.  The  diameter  of  the  shaft 
may  be  varied,  within  limits,  for  the  same  hub,  by  using  a  cone- 
key  of  the  proper  bore.  Perhaps  the  most  effective  application 
of  this  principle  is  the  Sellers  Double  Cone  Coupling  for  shafts, 
patented  and  manufactured  originally  by  William  Sellers  and 


*F.  R.  Jones  :   "Machine  Design,"  1899,  Part  II.,  p.  205. 


256 


MACHINE   DESIGN. 


Company.     As  shown  in  Fig.  106,  each  shaft,  as  A,  of  the  two  to 
be  connected  is  surrounded  by  a  hollow  cone,  B,  split  only  in  one 


FIG.  1 06. 

place.  The  cone  is  bored  to  fit  the  shaft  and  turned  to  a  taper 
corresponding  with  the  bore  of  one  end  of  the  encircling  shell 
or  "  muff,"  C.  The  cone-bushings  are  bound  to  the  shell  and 
shaft  through  friction  due  to  the  axial  stress  upon  three  bolts,  D,  of 
square  cross-section  which  lie  in  rectangular  slots  in  both  cones  and 
draw  the  latter  together  and  into  the  shell.  As  an  additional  pre- 
caution against  slipping,  each  cone  is  attached  positively  to  its 
shaft  by  a  sunk  key,  E.  The  taper  of  the  cones  is  about  I  :  7^-. 


FIG.  107. 

3.  KEYS  ON  THE  FLAT. — This  type,  Fig.  107,  is,  in  driving 
power,  intermediate  between  saddle  and  sunk  keys,  being  recessed 
in  the  hub  and  bedded  on  a  flat  planed  on  the  shaft.  The  upper 


KEYED   JOINTS  ;    PIN-JOINTS. 


257 


side  of  the  key  is  tapered.  Fastenings  of  this  character  were  used 
formerly,  as  in  Fig.  1070,  in  securing  large  hubs,  as  those  of 
paddle-wheels,  on  square  shafts.  In  such  cases,  the  keys  not 
only  lock  the  hub  in  place,  but  may  be  used,  within  limits,  to 
align  it  with  the  shaft. 

55.     Proportions  of  Keys. 

The  proportions  of  keys  and  key -seats  have  not  been  standard- 
ized and,  in  practice,  show  some  variation. 

i.  GENERAL  PROPORTIONS. — The  following  tables  give  the  pro- 
portions recommended  for  general  work  by  Mr.  John  Richards.* 
The  notation  refers  to  Figs.  99  and  100. 

TABLE  LXV. 

SQUARE  (STRAIGHT)  KEYS. 
(JOHN  RICHARDS.) 


Groove  in  shaft  should  be  T9^  T  in  depth.     Keys  should  not  bear  at  top  and  bottom. 

TABLE  LXVI. 


FLAT  (TAPER)  KEYS. 

(JOHN  RICHARDS.) 

D 

i 

1} 

i  f 

2 

2* 

3 

4 

5 

6 

7 

8 

W 

A 

A 

ft 

| 

1 

A 

i 
1 

I* 

if 

H 

1 

if 

i 

For  shafts  larger  than  those  given  in  the  table,  there  should  be  two  or  more  keys, 
the  width  of  which  may  be  \D  while  the  depth  may  be  obtained  by  making  angle 
0  =  30°. 

TABLE  LXVII. 

FEATHER  (SLIDING)  KEYS. 
(JOHN  RICHARDS.  ) 


D 

W 
T 
L 

1 

J 

i  f 

4 

* 

5 

3 

1 

9 

3j 

f 

ii 

t 

13 

4j 
15 

L  —  Maximum  length.     With  feather  fixed  in  hub,  the  shaft  key-  way  should  be  a 
little  the  deeper. 

*  "Manual  of  Machine  Construction,"  1889,  p.  57. 


258 


MACHINE   DESIGN. 


2.  SHAFTING.  —  Professor  Coleman  Sellers,  E.  D.,  gives  *  the 
following  proportions  : 

TABLE  LXVIII. 

KEYS  (SQUARE)  FOR  SHAFTING. 
(WILLIAM  SELLERS  &  Co.) 


Diameter  of  Shaft. 


Size  of  Key. 


A* 
A 


Length  of  key-seat  for  coupling  =  ij  X  nominal  diameter  of  shaft. 

3.  MACHINE  TOOLS. — The  following  tables  are  given  herein 
through  the  courtesy  of  Messrs.  William  Sellers  and  Company 
and  the  Brown  and  Sharpe  Manufacturing  Company  : 


TABLE  LXIX. 

KEYS  (SQUARE)  AND  KEY-SEATS  FOR  MACHINE  TOOLS. 
(WILLIAM  SELLERS  AND  Co.) 


Diameter  of  Shaft. 


I"  and  under. 

Over  \» 
I  '-'and  I?' 


2 
2 

4 
51 
7 
9 
ii 

13 


Size  of  Key. 


Size  of  Key-Seat 


*  "  The  Stevens  Indicator,"  IX.,  2. 


KEYED   JOINTS  ;    PIN-JOINTS. 

TABLE   LXX. 

KEY-WAYS  FOR  MILLING  CUTTERS. 
(BROWN  AND  SHARPE  MANUFACTURING  Co.) 


259 


Diameter  (D)  of  Hole. 

Width  (  W  )  of 
Key-way. 

Depth  (rf)  of 
Key-way. 

Radius  (tf). 

r  to  Ty 

A" 

*3/ 

.020" 

f          I 

H        i  i 

A 

ft 

.030 
•035 

iA         J  1 

T5 

A 

.040 

:(?    | 

2TV                2    i 

I 

t 

•3° 

.060 

.060 

*A           3 

A 

A 

.060 

4.  STATIONARY  ENGINES.  —  The  following  table  gives  the  prac- 
tice of  one  of  the  leading  builders  in  the  United  States  with  regard 
to  the  keys  (square)  for  cranks  and  the  flat  (tapered)  keys  for  the 
fly-wheels  of  stationary  engines  : 


TABLE  LXXI. 

ENGINE  KEYS. 


Diam.  of 
Shaft. 

Width  of 
Key. 

Thickness. 
T*:«™,    ~f 

Width  of 
Key. 

Thickness. 

Crank 
Key. 

Wheel  Key,       Shaft. 
Thin  End. 

Crank 
Key. 

Wheel  Key, 
Thin  End. 

3 

I 

A              J5 
16 

2f 

*f 

1 

3i 

A 

A 

3 

2\ 

| 

4 

8 

20 

Si 

2f 

5 

22 

3f 

3 

6 

I   3^ 

24 

3 

7 

jJL 

26 

4 

3 

I  1. 

{                     28 

3 

9 

I  |                   j 

30 

3 

10 

I  * 

i             32 

4 

ii 

ITS 

i               34 

4 

3 

12 

2yV                 1 

1              36 

5 

4 

3 

13 

2?                    ! 

1              38 

5| 

4 

3 

2| 

if              4o 

5f 

4 

3i 

260 


MACHINE    DESIGN. 


The  practice  of  this  company  is,  with  regard  to  : 
Crank- Keys  : 

(a)  No  taper  for  crank-keys. 

(b )  Key  to  be  \  in  shaft  and  \  in  hub,  measured  at  edge  of  key -way. 

(f  )   Use  2  keys,  set  90°  apart,  for  cranks  bored  23!  inches  diameter  and  above. 
(d)  Use  keys  for  nominal  diameter  of  shaft. 

(e  )   Keys  in  all  counterbalanced  cranks  to  be  on  the  diameter  passing  through  crank- 
pin,  but  on  the  opposite  side  of  shaft  from  the  pin. 

Fly -Wheels: 

(a)   Taper  of  key,  ^-inch  to  I  foot ;  tapered  side  in  hub. 

(£)    Thin  end  of  key  to  be  \  in  shaft  and  £  in  hub,  measured  at  edge  of  key- way. 

(f  )   Use  2  keys,  set  90°  apart,  for  shaft  15  inches  diameter  and  above. 

(d)  For  sizes  not  given  in  table,  use  key  for  next  smaller  shaft. 

5.  MARINE  ENGINES. — The   following    table   is    given  herein 
through  the  courtesy  of  the  Newport  News  Shipbuilding  and  Dry 
Dock  Company.     The  notation  (Fig.  100)  is  : 
D  =  diameter  of  shaft,  ins. 

W  =  width  of  key  and  key-way,  ins.  =  ^D  +  \". 
T=  thickness  of  key  =  -feD  +  \". 
t  =  depth  in  shaft,  measured  at  the  side. 
T  —  t  =  depth  in  hub,  measured  at  the  side. 
Taper  =  ^  in.  per  foot. 

TABLE  LXXII. 

KEYS    (TAPERED)    AND    KEY-WAYS,    MARINE   ENGINES. 
(NEWPORT  NEWS  SHIPBUILDING  AND  DRY  DOCK  Co.) 


KEYED   JOINTS;    PIN-JOINTS.  261 

Propeller  Keys.  —  The  hub  or  boss  of  a  screw-propeller  is  bored 
conically  and  fitted  accurately  to  a  corresponding  taper  on  the 
after -end  of  the  shaft,  the  latter  being  threaded  for  a  nut  which 
keeps  the  boss  in  place.  The  screw  is  driven  by  one  or  more 
longitudinal  keys  or  feathers  set  in  the  tapered  part  of  the  shaft 
and  fitting  into  suitable  key -ways  cut  in  the  boss.  These  keys 
meet  exceptionally  severe  service  in  rough  weather  when  the  ship 
is  pitching  and  the  position  of  the  screw  varies,  in  "racing,"  from 
partial  to  deep  immersion.  The  screw-propellers  for  U.  S.  naval 
vessels  are  now  made  of  manganese  bronze  or  approved  equivalent 
metal.  With  regard  to  the  proportions  of  keys  for  naval  pro- 
pellers, Lieutenant-Commander  F.  H.  Bailey,  U.  S.  Navy,  in 
charge  of  designs,  Bureau  of  Steam  Engineering,  Navy  Depart- 
ment, says  : 

"  These  keys  are  properly  feathers  since  they  are  not  usually  driven,  although  this 
has  been  done  in  the  case  of  some  torpedo-boats.  In  our  practice,  the  width  of  the  key 
is  about  one  and  a  half  times  its  thickness,  the  latter  being  such  that  the  side-pressure, 
calculated  from  the  maximum  turning  moment  on  the  shaft,  shall  not  exceed  about 
25,000  Ibs.  per  sq.  in.  on  the  propeller-hub.  Thus,  if  a  key  is  2  ins.  x3  ins.,  bears 
for  30  ins.  of  its  length,  and  is  half  in  hub  and  half  in  shaft,  the  bearing  surface  would 
be  30  sq.  ins.  If  the  mean  distance  of  the  key  from  the  centre  of  the  shaft  is  8  ins., 
the  maximum  turning  moment  on  the  shaft  could  be  30  X  *  X  2S>OO°  X  &  =6,000,000 
inch  pounds  which  maximum  moment  should  be  from  1.3  to  1.4  times  the  mean  turn- 
ing moment  calculated  from  the  horse-power  and  revolutions.  Usually,  we  design  the 
key  so  that  the  pressure  on  the  key-way  shall  be  about  22,000  Ibs.  per  sq.  in.  If  this 
pressure  gives  a  key  whose  thickness  is  over  £  of  the  shaft  diameter,  two  keys  set  oppo- 
site are  preferable." 

56.     Stresses  on  Keys. 

Keys  for  shafting  are  subjected  to  shearing  stress  on  the  longi- 
tudinal cross-section  and  to  crushing  stress  on  the  sides,  or,  when 
the  key  acts  as  a  strut,  in  the  direction  of  an  approximate  diagonal 
to  the  transverse  section.  As  a  general  rule,  it  is  better,  in  design- 
ing, to  follow  the  empirical  proportions  given  in  the  various  tables 
which  have  been  quoted,  since  keys  with  these  dimensions,  when 
well  fitted  and  driven,  seldom  fail  by  either  shearing  or  crushing. 
It  is  more  probable  that  the  shaft  will  be  sheared  or  that  the  key 
will  become  loose  in  its  seat  The  latter  action  is  soon  fatal  to 
-the  joint,  since,  through  lost  motion,  vibration,  and  shock,  the  key, 
if  not  secured,  will  back  out,  or  its  sides  or  those  of  the  key-seat 
will  become  so  battered  as  to  be  useless.  In  work  of  an  unusual 
nature  or  requiring  especial  care,  keys  may  be  designed  or  empir- 


262  MACHINE   DESIGN. 

ical  proportions  tested  by  the  application  of  the  principles  given 
below. 

Shearing  Stress  on  Key.  —  Let  P  be  the  load  on  the  crank-pin 
or  pulley-rim  ;  R,  the  lever-arm  of  that  load  from  shaft-centre  ;  D, 
the  diameter  of  the  shaft  ;  L,  the  length,  and  W,  the  width  of  the 
key  ;  and  Ss,  the  working  unit  shearing  stress  on  the  longitudinal 
cross-section.  Then  : 

Shearing  resistance  of  key  =L  x  W  x  St  ; 
Moment  of  key-resistance  =  L  •  W-  St  x  -£>/2  ; 
Moment  of  load  =  P  x  R. 

Equating  the  moments  : 


Since  the  length,  L,  of  the  hub  is  known,  the  minimum  value  of 
l¥may  be  obtained  from  (141). 

If  the  strength  of  the  key  against  shearing  is  to  be  equal  to 
that  of  the  shaft  in  torsion,  the  width,  W,  may  be  found  by  equat- 
ing the  resisting  moments  of  both.  Let  SJ  be  the  allowable 
shearing  unit  stress  at  the  circumference  of  a  solid  cylindrical 
shaft,  the  polar  modulus  of  the  section  being  Jjc.  Then  : 

Resisting  moment  of  shaft  =  S'  —  =  Sr  •  —  ^-  : 

1     c  16  ' 


. 

-=!•!•?•     I 

For  a  hollow  shaft  of  outer  and  inner  diameters,  Dl  and  d,  re- 
spectively, Jjc  becomes 


16          Dl 

and  the  leverage  of  the  key  is  DJ2. 

Crushing  Stress  on  Key.  — The  total  resistance  of  a  key  to  side- 
wise  crushing  is  equal  to  the  least  area  of  the  parts  of  the  side 
inset  in  shaft  or  hub,  multiplied  by  the  working  unit  crushing 


KEYED    JOINTS  ;    PIN-JOINTS. 


263 


stress,  Sc.  The  leverage  of  this  resistance  is,  as  before,  D/2,  ap- 
proximately. Assume  that  the  key  is  inset  one  half  the  depth,  T. 
Then: 

Crushing  resistance  of  key  =  L  x  T/2  x  S  ; 

Moment  of  key-resistance  =  L  •  T/2  •  Sc  x  DJ2. 

y 

Equating  this  moment  with  that  of  a  solid,  cylindrical/shaft  to 
torsion  : 


Equating  the  values  of  L  from  (142)  and  (143): 

*r>  ^J_         TTT 


(143) 


('44) 


which  values  apply  to  a  key  whose  strength,  in  shearing  and 
crushing,  is  the  same  and  is  equal  to  that  of  its  shaft  (solid,  cylin- 
drical) in  torsion.  If  Sc  =  2St,  we  have  T  =  W,  which  is  approx- 
imately true  for  square  keys.  For  flat  (taper)  keys,  which  drive 
as  a  strut  and  are  therefore  relatively  shallow,  Richard's  propor- 
tions (Fig.  100)  give  T  =  Wtan  30°.  The  crushing  action  on  the 
sides  is,  other  things  equal,  greater  in  square  keys  and  feathers. 
The  flat  key  is  wedge-shaped,  tends  to  drive  on  a  diagonal  to 
the  cross-section,  to  tip  in  the  seat,  and  thus  to  relieve  the  sides 
somewhat. 

W  *, 
'"1 


Shearing  Stress  on  Shaft. — The  load  on  a  square  key  or  feather 
acts  to  shear  the  shaft  on  the  plane  of  the  base  of  the  key-seat, 
i.  e.,  in  the  direction,  M-N,  Fig.  108.  Assume  that  the  unit 


264  MACHINE   DESIGN. 

shearing  resistances  of  shaft  and  key  are  the  same,  that  the  key  is 
sunk  l  Tin  the  shaft,  and  that  M-N  =  0-N  =  W.     Then  : 

.     T=2K-L=2(CK-CL\ 

Substituting  the  values  of  C-  K  and  C-L,  we  have,  with  sufficient 
approximation  : 


Neglecting  the  last  term  and  under  the  conditions  given,  the 
thickness  of  a  key  varies  directly  as  the  square  of  its  breadth. 
Hence,  since  the  shearing  resistance  varies  as  the  breadth,  the  use 
of  two  or  more  keys  in  the  place  of  one  is  attended,  considering 
shearing  stress  only,  by  a  reduction  in  the  total  metal  used  in  keys 
and  in  the  amount  slotted  out  for  key-ways. 

The  Grip  of  Friction  Keys.  —  The  holding  power  of  these  keys 
cannot  be  calculated  with  accuracy.  The  cone-key,  Fig.  109,  is 

driven  home  by  a  total  maximum 
£g^0^A  force,   Q,  which,  through  the  ex- 

pansion of  the  hub  and  the  com- 
IJI  pression  of  the  cone-bushing,  pro- 

duces the  normal  unit  pressure,  N, 
^4i  at  the  contact-surfaces  of  hub  and 

r  ^       key  and  the  radial   unit-pressure, 

.      ft,  %          \       p^  at  the  jomt  between  key  and 
T     shaft.     If  9  be  the  half  angle  of 
f       the    cone,   the    component    of  N 
FIG.  109.  which  is  normal  to  the  axis,  will  be 

Pl  =  Arcos  6.      Letting   L  =  axial 

length  of  bearing,  R^  =  mean  radius  of  outer  surface  of  cone, 
R^  =  radius  of  shaft,  and  JJL  and  //  =  coefficients  of  friction,  the 
resisting  moment  to  circumferential  slip  will  be,  between  : 

Resistance.  Moment. 

Shaft  and  bushing:  2xR0L  x  />  '>         ^~R^LP^  x  ^0  '> 
Bushing  and  hub  :     2~RVL  x  />'  ;        2-R^LPjt!  x  R^  ; 

which  moments  should  be  =  P.R,  the  turning  moment  on  the  shaft. 


*  Marks:   "Relative  Proportions  of  the  Steam  Engine,"  1896,  p.  97. 


KEYED    JOINTS;    PIN-JOINTS. 


265 


In  these  expressions,  the  surface  removed  in  dividing  the  bushing 
is  neglected.     At  the  instant  of  driving  home  : 


(2  (Max.) 


I  cos  ^ 


in  which  F  and  Fl  are  the  total  frictional  resistances  acting  along 
the  contact-surfaces.  While  Q  may  be  measured,  the  values  of  p 
and  p.'  ',  as  pointed  out  in  §4,  are  uncertain  in  such  cases.  Again, 
the  magnitude  of  P0  is  fixed  by  that  of  Pl  and  the  action  of  the  in- 
tervening metal.  Owing  to  the  slots,  the  bushing  cannot  strictly  be 
treated  as  either  a  thick  cylinder  or  a  thin  band.  In  fair  approxi- 
mation, the  grip  may  be  estimated  by  considering  the  cone  as  a 
hollow  cylinder  of  inner  and  outer  radii,  RO  and  Rv  respectively, 
subjected  to  the  external  pressure,  Pv 


57.     Through-Keys  :  Forms. 

The  through-key  (cross-key,  cotter)  is  simply  a  tapered  cross- 
bar of  rectangular  or  circular  section  driven  through  two  members 
to  be  joined,  as  the  sections  of  a  pump-rod,  a  piston-rod  and  piston, 
a  piston-rod  and  cross  head,  the  strap  and  body  of  a  connecting- 
rod,  etc.  The  joint  may  be  designed  to  resist  tension  only,  as  in 
foundation  bolts  ;  but  is  usually  adapted  for  both  tensile  and  com- 
pressive  stresses.  If  the  connected  parts  are  movable  axially  and 
the  key  is  sufficiently  long,-  the  latter 
gives  means  for  longitudinal  adjustment 
of  the  joint. 

(a)  Cross-keyed  Joints.  —  Fig.  1 10 
shows  such  a  joint  as  used  for  connect- 
ing the  piston  and  rod  of  a  locomotive 
engine.  The  rod  has  a  shoulder  at  A 
against  which  the  piston  is  driven  and 
on  which  it  bears  ;  its  end  has  a  sharp 
taper  (J  in.  in  4  ins.)  from  the  shoulder 
to  the  extremity,  B,  and  fits  in  a  conical 
hole  of  the  same  taper  in  the  piston,  C;  and  the  rod  and  piston 
are  joined  rigidly  by  a  key,  K,  whose  sides  are  parallel  and 
whose  top  has  a  taper  of  \  in.  in  12  ins.  The  sharp  taper  on 
the  rod  makes  the  parts  readily  detachable  when  the  key  is 
backed  out. 


FIG.  no. 


266 


MACHINE    DESIGN. 


In  Fig.  1 1 1  *  there  are  given  two  forms  of  a  similar  joint  be- 
tween the  piston  rods  and  crossheads  of  locomotive  engines.     In 


FIG.  in. 

that  to  the  left,  the  body  of  the  rod  is  reduced  for  the  taper  and 

the  crosshead  is  held  by  tension  upon  the  extremity  and  weakest 

part  of  the  rod,  while,  in 
the  other  type,  the  taper 
is  made  upon  an  enlarge- 
ment of  the  rod  and  the 
latter  bottoms  in  the  fit, 
the  joint  being  thus  made 
by  compressive  stress. 
The  latter  method  is  much 
more  secure  than  the  for- 
mer, in  which  the  tension 
invites  rupture. 

In  Fig.  112  a  similar 
connection  between  the 
sections  of  a  pump-rod  is 
shown.  A  socket,  G,  is 
formed  on  the  lower  sec- 
tion, E,  in  which  the  up- 
per section,  F,  is  re- 
cessed. Through  the 
socket  and  the  prolonga- 

*-j  *"  tion    of   the     upper    rod    a 

FIG    ii2  key -way    is    slotted.      The 

section,    F,    is    held    rigidly 

by  the  collar,  //",  formed  on  it  and  the  key,  K,  passing  through  it 

and  the  socket. 


*  American  Engineer  and  Railroad  Journal,  January,  1899. 


KEYED   JOINTS;    PIN-JOINTS. 


26; 


(ff)   Gib  and  Key  (Pig.  113).  —  The  brasses  of  the  connecting- 
rod  end  shown  in  this  figure  are  secured  in  place  by  the  key,  K, 


FIG.  113. 


and  gib,  G,  both  of  which  pass  through  parallel-sided  key-ways 
slotted  through  the  strap,  S,  and  the  body  of  the  rod.  The 
abutting  sides  of  gib  and  key  have  a  taper  of  ^  in.  to  ^  in.  in 
12  ins. 

As  the  key  is  driven  home,  the  gib  bears  on  the  inner  ends  of  the 
strap-slots  and  the  key  presses  against  the  outer  side  of  the  key- 
way  in  the  rod,  thus  drawing  the  brasses  firmly  together  and 
against  the  body  of  the  rod.  The  hooked  ends  of  the  gib 
overlap  the  strap  and  keep  it  from  spreading.  The  location 
of  the  center  of  the  journal  is  regulated  by  the  liners  between  the 
brasses  and  by  the  position  of  the  key.  The  latter  gives, 
therefore,  a  limited  range  of  adjustment  as  to  the  length  of 
the  rod. 

In  gib  and  key  joints  which  are  to  be  disconnected  frequently  or 
in  which  the  pressure  is  excessive,  the  key  may  be  tapered  on 
both  sides  and  pass  between  two  gibs  similar  to  G.  This  ar- 
rangement provides  increased  surface  of  a  durable  character  for 
the  key. 


268 


MACHINE    DESIGN. 


(V)  Bolted  Strap-Ends.  —  Fig.  1 14  and  Table  LXXIII.  give  the 
proportions  of  good  practice  in  bolted  strap-ends  for  connecting 


FIG.  114. 


rods,  a  form  which  is  more  modern  and  in  many  respects  more 
satisfactory  than  that  shown  in  Fig.  113.  In  this  type,  the  strap 
is  secured  by  bolts,  G,  passing  through  it  and  the  body  of  the 
rod,  while  the  key,  N,  becomes  a  wedge  simply  which  forces  the 
brasses  together  and  against  the  outer  end  of  the  strap.  The 
taper  (8  degrees)  of  the  key  is  considerable  and  the  position  of  the 
latter  is  regulated  by  the  bolt,  O,  passing  through  it  and  through 
both  forks  of  the  strap. 

(d}  Taper  Pins.  —  In  light  work,  taper-pins  are  frequently  used 
as  cross-keys,  as,  for  example,  when  driven  into  a  diametrical 
hole,  drilled  and  reamed  {p  a  corresponding  taper,  through  the 
hub  and  shaft  of  a  gear-wheel.  The  dimensions  of  the  standard 
taper-pins  made  by  the  Morse  Twist  Drill  and  Machine  Co.,  are  : 


Number. 

0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

10 

Diameter  at  Large 
End,  Inches. 

.156 

.172 

•193 

.219 

.250 

.289 

•341 

.409 

492 

•591 

.706 

Approximate  Frac- 
tional Sizes. 

A 

tt 

T3* 

A 

i 

it 

a 

if 

\ 

H 

If 

The  taper  is  ^  in.  per  foot.  The  length  ranges  from  |  in.  for 
the  No.  o  to  6  ins.  for  the  No.  10,  in  increments  of  |-  in. 

0)  Split  Pins  (Table  LXXVL). —These  pins  may  be  used  to 
prevent  endwise  motion  in  a  nut  or  a  pin-joint.  They  are  circu- 
lar in  section,  cylindrical  or  tapering  in  form,  and  are  either  split 
throughout,  except  at  the  head,  or  at  the  end  only.  When  driven 
home,  the  pin  is  locked  by  spreading  the  split  end. 


KEYED   JOINTS;    PIN-JOINTS. 


269 


X   §  2 
X  <§£ 

-  Is 
3j* 


Diam. 
of  Cylinder, 
Inches. 


CO    O   <N   ^J-\O  CO 


\O  CO    O   M   Tj-vO  OO    O   N   -^"VO  03 


>OVO  vb  vo"t^  t-CO  &>'  O^O*  O 


>  lO^O  VO  VO  t~*  t~-00   ON  OS  O    O    M   <-> 


CO  -=fr  -<t  >O 


O    "-*    CO  ^  ^}"  iO  t^.GO    ON  O    *-"    CN    rO  ^"  LO^O 

MMMt-!l-ll-(MMI-((N<NCS<NMtS<N 


J^JSHWHOHB.^- 


Diam. 
Cylinder, 
Inches. 


2/0  MACHINE   DESIGN. 

58.     Through-Keys  :  Stresses. 

i.  TENSILE,  SHEARING,  AND  BEARING  STRESSES.  —  Assume  the 
joint,  Fig.  112,  to  be  stressed  axially  and  alternately  in  opposite 
directions.      Failure  may  occur  by  : 
Tensile  Stress  : 

(a)  On  sections,  E  or  F\  (ft)  on  section,  Z,  where  reduced  by 
the  keyway  ;  (c)  on  socket,  G,  where  similarly  reduced  ;  (d}  on 
the  key,  due  to  bending. 
Shearing  Stress  : 

(e)  On  the  key  at  inner  surface  of  socket,  G  ;  (/)  on  socket,  G, 
above  key;  (g)  on  collar,  H  ;  (/i)  on  section,  L,  below  key. 
Bearing  Stress  : 

(fc)  On  key  ;  (/)  on  section,  L  ;  (?#)  on  socket,  G  ;  («)  on 
collar,  H. 

Take  St,  St  =  o.8^S(,  and  Sh  as  the  permissible  unit  tensile,  shear- 
ing, and  bearing  stresses,  respectively.  The  exact  manner  in 
which  the  key  is  loaded,  is  unknown.  Assume  it  to  be  a  simple 
beam,  uniformly  loaded  with  total  stress,  P.  Then  for  condition  : 


(b) 
(c) 


0)  P=2(b-h-St); 

(/)  P=2(D-d)hl.St 

(g)  P=xJ./is-S,; 

(h]  P=2(d-/i2-St); 

(k)  P=b-d-S,- 


(») 


KEYED   JOINTS;    PIN-JOINTS.  271 

It  is  evident  that  the  more  important  of  these  stresses  are  shown 
by  (<*)»  00  and  (0-     Taking  S.  =  o.SSt  and  equating  (d)  and  (e)  : 

btf 
%'~d°  S<=  I-6A&-S;; 

h=l.2d.  (I45) 

Substituting  in  (e)  and  equating  (ff)  and  (e)  : 


i.c>2bd-S  =    -d- 

b  =  o.2?d,  say  0.25^  (I46) 

a  ratio  which  conforms  with  good  practice.  The  value  of  D  in 
terms  of  d  may  be  found,  for  tensile  stress,  by  equating  (b)  and  (c) 
and  making  b  =  o.2$d.  This  value,  however,  is  less  than  that  for 
bearing  pressure  obtained  by  equating  (/)  and  (in).  From  the 
latter  equations  : 

D=2d.  (,47) 

Equating  the  tensile  and  bearing  resistances,  (b}  and  (/),  respec- 
tively, of  rod  L  : 


.'.^=2.14,  (148) 

a  ratio  which  is  not  excessive  with  good  materials  and  fitting.  The 
depths,  /^  and  hv  if  calculated  for  shearing  simply  by  (/)  and  (//), 
are  less  than  is  required  by  good  practice.  Their  value  is  usually 
from  d  to  1.25^,  with  wrought  iron.  The  diameter  d2,  of  the  col- 
lar, H,  should  be  greater  proportionately  in  small  rods,  since  the 
fillets  and  rounding  greatly  reduce  the  bearing  surface.  Taking 
the  unit  bearing  pressure  upon  the  collar  as  |5ft,  we  have,  from 
(/)  and  (n)  with  b  =  dJ4: 


i.22d.  (149) 


2/2  MACHINE    DESIGN. 

Equating  (e)  and  (g}  and  substituting  the  values  of  b  and  h : 


z  =  o.2d,  about, 


(ISO) 


a  height  which,  considering  the  fillet  of  the  collar,  is  sufficient. 

2.  DRIVING  FORCE  ON  KEY. —  Let  A  and  B,  Fig.  115,  be  two 
members  of  the  same  material  united  by  a  through-key,  C,  one  side 

of  the  latter  having  the 
angle  of  taper,  6.  Take 
IVas  the  axial  load  upon 
the  joint  and  /z  and  <p  as 
the  coefficient  of  friction 
and  angle  of  repose, 
respectively,  of  C  and  A 
jf  or  B.  Then,  disregard- 

ing the  friction  between 
the  members,  A  and  B,  in : 
(a)  Driving  home  the 
key,  the  latter  is  acted 
upon  by  the  driving 
force,  P,  and  the  reac- 
tions, R  and  Rv  devel- 
oped at  the  contact-sur- 
faces by  the  load,  W. 
The  force,  P,  is  opposed 
by  the  horizontal  com- 
ponents of  these  reac- 
tions. 

At  the  contact-sur- 
faces of  B  and  C,  the 
load,  W,  taken  as  con- 
centrated at  0,  produces 
the  total  normal  pressure, 
N,  which  pressure,  when 

the  key  moves,  develops  the  force  of  friction,  F  —  fjtA7  =  N 
tan<f.  The  reaction,  R,  is  the  resultant  of  N  and  F  and  is 
hence  inclined  from  N  and  toward  P  by  the  angle  <p,  and  from  the 
vertical  by  the  angle  <p  +  6.  The  horizontal  component  of  this 
reaction  is  R  sin  (<p  +  0). 


KEYED   JOINTS;    PIN-JOINTS.  2/3 

The  load,  W,  is  divided  between  the  two  forks  of  member,  A. 
Consider  it  as  concentrated  at  D,  at  which  point  it  produces  a  total 
normal  pressure,  Nv  and,  when  the  key  moves,  a  force  of  friction, 
Fl  =  pNl  =  NI  tan  <p,  and  a  reaction,  Rv  inclined  toward  P  and 
from  TVj  and  the  vertical  by  the  angle  <p.  The  horizontal  compo- 
nent of  this  reaction  is  Rl  sin  if.  Hence  : 

P=Rsin(y>  +  0)  +  R^iny;  (151) 

but,  R=Wj  cos  (<p  +  6}     and     Rl  =  NJ  cos  y>  =  Wj  cos  <p 

+  0)  +  tanp].  (152) 


(£)  /#  backing  out  the  key,  consider  the  load  as  concentrated 
at  0  and  E  with  regard  to  the  members,  B  and  ^4,  respectively. 
The  conditions  are  as  before,  excepting  that  the  forces  of  friction, 
F'  and  F^  ,  act  toward  the  backing  force  P'  .  Therefore,  the  reac- 
tion, R'  ,  is  inclined  from  the  vertical  and  toward  P'  by  the  angle 
(<p  —  0)  and  the  reaction,  R^  ,  by  the  angle  (p.  Hence,  as  in  (i  52)  : 

/>'=  JF[tan(ip-0)  +  tanp].  (153) 

,    (c)  Maximum  Taper.  —  If  the  angle  6  is  so  great  that  the  key, 
when  driven  home,  is  on  the  point  of  backing  out,  P'  =  O.     Hence, 

tan  (<p  —  6)  -f  tan  <p  =  o 
and 

0=  2<p, 

which  is  the  limiting  value  for  0,  when  the  key  is  not  fitted  with 
set-screws  or  other  locking  devices. 

(d}  Friction  of  Members.  —  The  preceding  equations  neglect 
the  friction  between  the  members,  A  and  B,  and  the  value  of  W 
is  therefore  greater  than  the  given  force,  P  and  P',  would  over- 
come in  practice.  Let  Wf  be  the  axial  load,  considering  this  fric- 
tion. Then  (Fig.  1  1  5)  the  reaction,  R,  will  produce,  between  the 
contact-surfaces  of  A  and  B,  a  force  of  friction, 


which  force  will  act  downward  in  driving  home.     Hence,  in  raising 
B,  the  vertical  loads  to  be  overcome  are  : 

Wf  +  {Ji.fi  sin  (<p  +  0), 


2/4  MACHINE   DESIGN. 

which  quantity  must  be  substituted  for  W  in  preceding  equations. 
Hence,  considering  the  friction  between  the  connected  members  : 

Wsm+e  W 


cos  (  <p  4-  6)  cos  (<f>  +  6)  —  fJLz  sin  (y  +  6}  ' 

(f  +0) 


1  cos  tp 

Substituting  in  (151)  : 

P=  [  Wf  +  fjtyR  sin  (ip  +  0)]  [tan  (p  +  (?)  +  tan 
tan  (p  +  0)  +  tan  y 


in  which  /^2  is  the  coefficient  of  friction  for  the  metal  of  A  and  ^. 
In  finding  the  value  of  P'  by  a  similar  method,  the  force  of  friction 
is  calculated  from  the  normal  pressure  produced  by  R'  and  that 
force  acts  upward,  in  opposition  to  Wf,  and  hence  is  subtractive. 

(i)  Double  Taper.  —  Assume  that  both  sides  of  the  key  have 
the  same  angle  of  taper,  6,  as  shown  by  broken  lines  in  Fig.  115. 
Then,  Rl  and  R^  are  equal  to  R  and  R'  ',  respectively,  and,  from 
(1  52)  and  (153): 

6);  (155) 

6),  (156) 

which  equations  neglect  the  friction  of  the  connected  members. 

The  limiting  angle  of  taper  at  which  this  key,  when  driven 
home,  is  on  the  point  of  backing  out,  is  found,  as  before,  by 
making  P'  =  o.  Hence  : 

tan  (<p  —  6)  =  o  .-.  6  =  tp. 

Under  customary  conditions,  with  slightly  oily  metals  and  with- 
out locking  devices  on  the  key,  the  latter  will  begin  to  back  out 
when  its  taper  reaches  about  I  -\  ins.  per  ft,  i.  e.,  a  ratio  of  I  to  8. 
The  taper  for  such  keys  is,  in  practice,  much  less,  the  ratio  being 
usually  5  or  6  times  this  limit. 

59.     Pin-Joints. 

Pin-joints,  i.  e.,  those  in  which  two  or  more  members  are  united 
pivotally  by  a  cylindrical  pin  meet  frequent  use. 


KEYED   JOINTS;    PIN-JOINTS. 


275 


I.   BOILER  BRACES.  —  The  joint  may  be  as  shown  in  Fig.  116 
or  the  member,  B,  may  be  replaced  by  a  lug  or  curved  strap  pass- 


e^d 

FIG.  116. 

ing  over  the  pin  and  riveted  to  the  head-plate.  In  such  a  joint, 
if  the  parts  be  accurately  fitted  without  lost  motion  between 
members,  A  and  B,  or  between  the  pin-bearing  and  pin,  the  latter 
is  subject  only  to  double  shear.  The  fit,  however,  is  frequently 
loose  ;  and,  in  any  event,  the  pin  and  bearing  will  probably  wear. 
Hence,  the  pin  is  subject  frequently  to  both  shearing  and  bending 
stresses  and  may  fail  as  shown  in  Fig.  117.* 


FIG.  117. 

(a)  Brace-body.  —  In  general,  let  L  be  the  length  and  B  the 
breadth  in  ins.  of  the  area  supported  by  the  brace  and  let  p  be  the 
pressure  per  sq.  in.  upon  that  area.  Then  the  total  load  on  area 
and  brace  is  : 

(157) 


in  which  St  is  the  working  unit  tensile  stress  of  the  brace. 
*  The  Locomotive,  August,  1901. 


270  MACHINE   DESIGN. 

(ft)  Shearing  Stress  on  Pin.  — Assuming  accurate  fitting  through- 
out, the  pin  will  be  subject  only  to  double  shear.  Then,  by  §45, 
3,  and  taking  Ss,  the  mean  unit  shearing  stress,  as  0.8 St: 

W=  1.75  --d2l4-Ss  =  i.4-xd2/4-St.  (1S&) 

Equating  (157)  and  (158) : 


(c)  Bending  Stress  on  Pin.  —  The  distribution  of  the  load  upon 
the  pin,  in  its  bearings  both  in  B  and  in  the  forks  of  A,  is  unknown. 
In  any  event,  the  pin  acts  as  a  supported  beam  of  circular  cross- 
section,  as  in  Fig.  118.  In  extreme  cases,  the  load,  Wt  may  be 


FIG.  1 1 8. 


concentrated  at  the  centre  of  the  length,  and  the  distance,  /, 
between  the  supports  maybe  the  total  width,  C-£,  Fig.  1 16,  of  the 
bearing.  Assume  /  =  i.$d and  the  load  as  concentrated,  as  above. 
Then,  the  maximum  bending  moment  is  : 


in  which  Ife  is  the  modulus  of  the  section.     Then  : 

W=i~J*-Sf  (159) 

Taking  the  tensile  stress  due  to  bending  as  equal  to  that  in  direct 
tension  and  equating  (157)  and  (159)  : 

d=   1.2D. 

For  average  practice,  the  diameter  for  shearing,  as  thus  calculated, 
is  too  small  and  that  for  bending  is  large.     Taking  the  mean  : 
d  =  D. 


KEYED   JOINTS;    PIN-JOINTS.  277 

(d)  Sides  and  Crown  of  Eye.  —  When  the  diameter  of  the  pin  is 
such  that  the  eye  may  be  tested  to  destruction,  the  latter  fails  by 
crushing  at  h,  Fig.  116,  and  rupture  at  the  two  sections,  b,  the 
metal  flowing  so  that  the  thickness  of  the  eye  is  increased  consid- 
erably at  the  inner  limit  of  h  and  much  decreased  at  those  of  b, 
where  fracture  appears  first. 

The  section  at  b  is  subjected  not  only  to  tensile  stress  due  to  its 
share  of  the  load,  W,  but  also  to  an  additional  bending  stress, 
owing  to  the  distance  between  the  line  of  application  of  the  load 
and  the  centre  of  gravity  of  the  section.  With  regard  to  the  width 
of  the  crown  at  h,  the  problem  is,  in  general,  one  of  indentation 
(p.  184)  and  the  stresses  (§  45,  46)  resemble  somewhat  those  in  a 
thick,  hollow  cylinder  under  internal  fluid  pressure.*  The  case  is 
also  similar  generally  to  that  of  the  margin  of  a  riveted  joint,  in 
which,  for  ample  strength  E=  i.$d  (84),  i.  e.,  the  distance  from 
edge  of  hole  to  edge  of  sheet  is  d.  In  practice  the  periphery  of  the 
eye  is  concentric  with  the  hole  and  h  =  b  =  o.$d  to  0.7 $d. 

(e)  Member  A.  —  The  thickness,  /,  of  the  forks  should  be  pro- 
portioned for  two  thirds  of  the  load  to  allow  for  inaccurate  fitting 
and  irregular  distribution.      Generally,/=  0.66^  to  0.75^. 

In  good  work,  bosses  for  planing  are  formed  on  each  side  of  the 
eye  and  where  the  head  and  washer  of  the  pin  fit,  with  a  conse- 
quent increase  of  thickness  at  those  points. 

(/)  Tests.  —  In  1879,  Chief  Engineers  Sprague  and  Tower,  U. 
S.  Navy,  made  exhaustive  experiments  upon  boiler  braces.  Their 
recommendations  t  are  : 

"The  following  is  submitted  for  the  proportions  (with  sufficient  excess  in  the  eye  for 
wear,  etc.)  of  the  ends  of  boiler  braces  made  in  the  manner  specified.  In  the  same 
bar,  the  section  across  the  eye  must  be  increased  with  each  material  increase  of  the 
diameter  of  the  pin.  When  the  brace  is  round  and  the  thickness  of  the  eye  and  the 
diameter  of  the  bar  are  equal,  let  .r  =  areas. 

"  For  ends  made  by  drawing  out  the  bar,  bending  it  around  and  welding  :  x  =  width 
of  bar  and  the  diameter  of  iron  pin,  ^  j-  x  =  diameter  of  steel  pin,  |  x  =  breadth  of 
(concentric)  eye,  thickness  of  eye  to  equal  that  of  bar. 

"  For  ends  cut  from  flat  bars,  x=  width  of  bar  and  diameter  of  iron  pin,  f  x  =  di- 
ameter of  steel  pin,  f  x  =  breadth  across  each  side  of  eye,  |  x  =  depth  through  crown 
of  eye,  thickness  of  eye  =  that  of  bar. 

"For  ends  upset,  and  forged  solid,  holes  drilled,  x  =  area  of  bar  and  area  of  iron 
pin,  1.48.*—  area  of  section  across  the  eye,  .9^  =  area  through  crown  of  eye." 

*Cotterill:  "  Applied  Mechanics,"  1895,  p.  368. 

f"  Report  on  Experiments  to  Ascertain  Proportions  for  the  Ends  of  Boiler  Braces," 
Washington,  1880. 


278 


MACHINE    DESIGN. 


2.  STRUCTURAL  WORK.  —  Pin-joints  are  used  for  trusses  and  in 
the  lateral  system.     One  such  joint  is  shown  in  Fig.  119,  which 


- 

f 

1 
1 

f 

f 
\ 
T 

J 

I 
| 

3" 

2.7. 

ft 

4  li 

I 

t/&yJ^.  
Men\ber 

i 

i 
1 

- 

FIG.  119. 

has  a  compound  member  in  the  centre  with  four  sets  of  eye-bars 
in  pairs,  one  bar  of  each  pair  being  on  each  side  of  the  centre. 
Large  pins  have  a  nut  at  each  end ;  those  of  smaller  diameter 
may  have  a  head  at  one  end  and  a  split-pin,  serving  as  a  cotter, 
at  the  other.  To  allow  for  irregularities  in  thickness  or  fit,  the 
"grip,"  or  length  of  pin  between  the  inner  faces  of  the  nuts,  is 
increased,  beyond  the  aggregate  thickness  of  the  connected  mem- 
bers, by  ^g  in.  for  each  bar  and  ^  in.  for  the  riveted  member  as  a  rule. 

The  stresses  on  the  bars  and  pin  may  be  horizontal,  vertical, 
or  diagonal.  Resolving  the  latter  into  horizontal  and  vertical 
components,  the  pin-stresses  may  be  divided  into  four  classes  : 
Positive  horizontal  and  negative  horizontal  stresses,  acting  toward 
the  left  and  right,  respectively ;  and  positive  vertical  and  negative 
vertical  stresses,  acting  upward  and  downward,  respectively.  The 
pin,  Fig.  119,  may  be  considered  as  a  beam,  acted  upon  by  various 
stresses,  as  above,  each  at  a  distance  from  the  next  stress  corre- 
sponding with  the  thicknesses  of  the  respective  eye-bars  and  the 
allowance  for  irregularities.  The  diameter  of  the  pin  must  be 
proportioned  for  bending,  shearing,  and  bearing  pressure. 

(a)  Bending.  —  If  the  maximum  bending  moment  on  the  pin  be 
known,  the  diameter  of  the  latter  for  bending  stress  may  be  found 
from  the  fundamental  formula  : 

J/(max)  =  5-7  =  5.  — 

c  32  ' 

in  which  M  is  the  maximum  moment,  5  is  the  allowable  working 
unit  stress,  and  d  is  the  diameter  required. 


KEYED   JOINTS;    PIN-JOINTS.  279 

To  determine  the  maximum  moment  for  any  given  manner  of 
loading,  the  moment  at  the  centre  of  each  member  must  be  found, 
each  load  being  considered  as  concentrated  at  the  centre  of  its 
respective  bar.  This  moment  will  be  the  resultant  of  all  preceding 
moments  to  the  left.  The  principles  of  the  resolution  and  com- 
position of  forces  apply  also  to  moments.  Hence,  the  moment 
upon  any  section  will  be  the  resultant  of  the  horizontal  and  verti- 
cal moments  upon  that  section,  i.  e.,  the  square  root  of  the  sum 
of  the  squares  of  the  latter  moments. 

Thus,  assume  in  Fig.  1 19,  stresses,  />,  />,  Py  />,  upon  the  cor- 
responding members,  the  lines  of  action  being  separated  by  the 
distances,  av  a2,  ay  Let  Pl  be  a  positive  horizontal  stress  ;  Pv  a 
diagonal  stress  with  vertical  and  horizontal  components,  +  Pp 
and  —  PJi,  respectively ;  Py  a  diagonal  stress  with  vertical  and 
horizontal  components,  —  P3v  and  —  PJi,  respectively  ;  and  PI  a 
negative  vertical  stress.  Then  at : 

Member  No.  ^  .• 

Horizontal  Moment  =  Pl  x  al 
Vertical  "       =  o ; 


Resultant          "       =  V  H.  M22  -f  o  =  H.MV 


Member  No.  j  : 

Horizontal  Moment  =  Pl  (a^  -f-  a^)  —  PJi  x  tf  2  = 
Vertical  "        =  P2v  X 

Resultant  "        = 


Succeeding  resultant  moments  may  be  calculated  similarly. 
From  a  comparison  of  the  results,  the  value  and  location  of  the 
maximum  bending  moment  upon  the  pin  may  be  found.  Table 
LXXIV.  gives  the  required  diameters  for  various  maximum  mo- 
ments and  extreme  fibre  stresses  per  sq.  in.,  as  computed  by  the 
fundamental  formula  for  bending  moment.  It  will  be  observed 
that  the  calculations,  as  above,  apply  only  to  the  pin  before  bend- 
ing. When  the  latter  occurs,  the  stress-leverages  and  maximum 
moment  are  reduced. 


280 


MACHINE   DESIGN. 


TABLE  LXXIV. 
MAXIMUM  BENDING  MOMENTS  ON  PINS. 


Pin. 

Moments  in  Inch  Pounds  for  Fibre  Strains  per  Square  Inch  of 

Diam.           Area. 

15,000 

18,000 

20,000             22,000 

*S,ooo 

I  " 

0.785 

1,470 

1,770 

1,960 

2,160 

2,450 

ij 

1.227 

2,880 

3>45o 

3,830 

4,220 

4,790 

If 

1.767 

4.970 

5,96o 

6,630 

7,290 

8,280 

l£ 

2.405 

7,890 

9-470 

10,500 

H,570 

13,200 

2 

3-I42 

11,800 

14,100 

I5,7oo 

I7,28o 

19,600 

2i 

3-976 

16,800 

20,100 

22,400 

24,600 

28,000 

•2\ 

4.909 

23,000 

27,600 

30,700 

33,700 

38,400 

2i 

30,600 

36,800 

40,800 

44,900 

51,000 

3 

7.069 

39,800 

47,700 

53,ooo 

58,300 

66,300 

8.296 

50,600 

60,700 

67,400 

74,100 

84,300 

3i 

9.621 

63,100 

75,800 

84,200 

92,600 

105,200 

3f 

H.045 

77,700 

93,200 

103,500 

113,900  j      129,400 

4 

12.566 

94,200 

113,100 

125,700 

138,200         157,100 

4* 

I4.l86 

113,000 

I35,7oo 

150,700 

165,800 

188,400 

3 

I5-904 
17.721 

134,200 
157,800 

161,000 
189,400 

178,900 
210,400 

196,800 
231,500 

223,700 
263,000 

5 

I9-635 

184,100 

220,900 

245,400 

270,000 

306,800 

5t 

21.648 

213,100 

255,700 

284,  100 

312,500 

355,2oo 

5* 

23.758 

245,000 

294,000 

326,700 

359,3oo 

408,300 

1* 

25-967 
28.274 

280,000 
318,100 

335,900 
381,700 

373,300 

424,  TOO 

410,600 
466,500 

466,600 
530,200 

6J 

30.680 

359,500 

431,400 

479,400 

527,300 

599,200 

6J 

33-I83 

404,400 

485,300 

539,200 

593,ioo 

674,000 

6f 

35.785 

452,900 

543>5oo 

603,900 

664,200 

754,800 

7 

38.485 

505,100 

606,100 

673,500 

740,800 

841,900 

7i 

41.282 

561,200 

673,400 

748,200 

823,000 

935,300 

7i 

44-179 

621,300 

745,5oo 

828,400 

911,200 

1,035,400 

7! 

47-173 

685,500 

822,600 

914,000 

1,005,300 

1,142,500 

8 

50.265 

754,000 

904,800 

1,005,300 

1,105,800 

1,256,600 

8| 

53456 

826,900 

992,300 

1,102,500 

1,212,800 

1,378,200 

8* 

56.745 

904,400 

,085,200 

1,205,800 

1,326,400 

1,507,300 

8J 

60.132 

986,500 

,183,800 

1,315,400 

1,446,900 

1,644,200 

9 

63.617 

,073,500 

,288,200 

1,431,400 

i,574,5oo 

1,789,200 

9t 

67.201 

,165,500 

,398,600 

1,554,000 

1,709,400 

1,942,500 

9i 

70.882 

,262,600 

,5i5,ioo 

1,683,400 

1,851,800 

2,104,300 

9f 

74-662 

,364,900 

,637,900 

1,819,900 

2,001,900 

2,274,900 

10 

78.540 

,472,600 

,767,100 

1,963,500 

2,159,900 

2,454,400 

loj 

82.520 

,585,900 

,903,000 

2,114,500 

2,325,900 

2,643,100 

loj 

86.590 

,704,700 

2,045,700 

2,273,000 

2,500,200 

2,841,200 

lof 

90.760 

,829,400 

2,195,300 

2,439,300 

2,683,200 

3,049,100 

ii 

95.030 

,960,100 

2,352,100 

2,613,400 

2,874,800     3,266,800 

ii  \ 

99400 

2,096,800 

2,516,100 

2,795,700 

3,075,400     3,494,800 

til 

103.870 

2,239,700 

2,687,600 

2,986,300 

3,284,800     3,732,800 

iif 

108.430 

2,388,900 

2,866,600 

2,185,200    3,503,700  :  3,981,500 

12 

II3.IOO 

2,544,700 

3,053,600 

3,392,900      3,732,190  ;  4,241,200 

(£)  Shearing.  —  The  vertical  shear  at  any  section  of  the  pin  is 
the  algebraic  sum  of  the  vertical  stresses  to  the  left  of  that  section. 
Similarly,  the  horizontal  shear  at  the  section  considered  is  the 
algebraic  sum  of  the  horizontal  stresses  to  the  left  of  that  section. 
Then,  the  resultant  shear  upon  the  section  is  the  square  root  of 


KEYED   JOINTS;    PIN-JOINTS.  28 1 

the  sum  of  the  squares  of  the  vertical  and  horizontal  shears,  as 
above.     Thus,  the  shears  are  at : 

Member  No.  j  : 

Horizontal  =  />  -  PJi  =  H.S3 ; 
Vertical       =  o  +  P2v  =  V.S^\ 


Resultant  =  VH.S*  +  V.S* 


While,  in  a  cylindrical  section,  the  maximum  is  £  the  mean  shear- 
ing stress  (p.  182),  it  is  usual  to  consider  the  shearing  stress  on 
pins  as  uniformly  distributed  over  the  cross-section.  Again,  since 
the  bars  are  in  pairs,  the  pin  may  be  considered  as  under  double 
shear.  Hence,  for  one  pair  of  bars  : 


in  which  R.S.  is  the  maximum  resultant  shear,  as  above,  d  is  the 
diameter  required  to  withstand  that  shear,  and  S^  is  a  unit  work- 
ing shearing  stress  which  is  low  enough  to  permit,  with  safety, 
the  excess  of  maximum  over  mean  stress. 

(c)  Bearing.  —  The  ranges  of  permissible  bearing  pressure  and 
shearing  stress  have  been  given  previously  (p.  224). 

(d}  Proportions.  —  Table  LXXV.  gives  the  proportions  of  pins 
with  Lomas  nuts  and  Table  LXXVI.  of  pins  with  cotters.  The 
latter  are  used  with  pins  of  small  diameters  only.  The  former  are 
preferable,  since  the  nut  is  recessed  and  bears  only  on  its  periph- 
ery. This  allows  the  body  of  the  pin  to  enter  it  and  enables  it  to 
be  set  up  tightly  when  the  aggregate  thickness  of  the  members 
with  the  allowances  is  not  equal  to  the  estimated  grip  of  the  pin. 

(e)  Eycbars.  —  The  proportions  of  plain  and  adjustable  eye-bars 
are  given  in  Table  LXXVII. 

(/")  Specifications.  —  The  following  extracts,  referring  to  pin- 
joints,  are  taken  from  the  specifications  of  the  American  Bridge 
Company  for  steel  railroad  bridges.  The  specifications  for  rivet, 
soft,  and  medium  steel  are  given  on  page  219. 

'  '  Pins  made  of  either  of  the  above  mentioned  grades  of  steel  shall,  on  specimen  test- 
pieces  cut  from  finished  material,  fill  the  requirements  of  the  grade  of  steel  from  which 
they  are  rolled,  excepting  the  elongation,  which  shall  be  decreased  5  per  cent,  from 
that  specified. 

"  Pins  up  to  7  inches  diameter  shall  be  rolled. 


282 


MACHINE   DESIGN. 


TABLE  LXXV. 

PINS  WITH  LOMAS  NUTS. 
(AMERICAN  BRIDGE  Co.) 


P 

la. 

3 

Mut. 

11 

Ii 

Set 

ew. 

Di£ 

m. 

•s 

3* 

1 

Diam. 

Len 

gth 

Ad 

G 

i  to 
ip. 

.c 

Ro 
He 

t 

She 
Dia 
•      Jj 

rt 
m. 

Lo 
Dij 
j 

ng 
in. 

• 

II 

H 

J 

K 

2" 

$" 

r 

if 

» 

X1 
^ 

gf 

3 
3 

ff 

3 

3 

i" 

2-5 
2-5 

2} 

2H 

I 

i 

3 

4, 

V 

2.5 

1} 

I 

\ 

2f 

ail 

I 

i 

3 

4 

b 

2.5 

3 

3yj 

i 

«1 

V 

4 

5 

3 

3i 

3y*2 

I 

«1 

4 

5i 

V 

3 

3* 

3j| 

\ 

2^ 

^ 

4! 

* 

J. 

3 

3* 

3f  1 

3 

2 

i 

5 

5 

5-5 

4 

4s  z 

3 

r 

2 

;! 

5 

5 

5-5 

3 

4?  z 
4H 
4ff 

1 

, 

\ 

3: 
3\ 

? 

5 
5 
5 

6 
6 
6 

7 
7 

If 

Bj 

\ 

5 

5yV 

4 

3 

^ 

6 

7 

8.5 

5i 

5sz 

4 

3! 

6 

7 

8-5 

5* 

sH 

4* 

4: 

I 

7 

8 

[ 

ii 

4i 

i 

7 

8 

r 

ii 

1 

i 

5 
5 

i 

j 

7 

7 
7i 

8 

r 

ii 

12 
12 

7 

7?I 

1 

5i 

V 

00000000 

9 
9 

9 
9 

13-5 

13-5 
13-5 

7l    ; 
8 

i 

6 
6 

i 

5 
5 

9 
9 

10 
10 

17 

17 

8J 

6 

• 

5 

9 

10 

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2* 

1\ 

\ 

8^ 

84? 

6 

* 

5 

Q.- 

10  , 

8|     i 

8ff 

6 

2 

5 

i 

IoJ 

12  j 

9 

9A 

6 

a 

5 

IOJ 

12  1 

6 

3 

5 

1 

IOJ 

I?i 

10 

41 

NOTE. — To  obtain  grip  G  add  TJ5  for  each  bar,  together  with  amount  given  in  table. 


KEYED   JOINTS;    PIN-JOINTS. 


283 


"  Pins  exceeding  7  inches  diameter  shall  be  forged  under  a  steel  hammer  striking  a 
blow  of  at  least  5  tons.  The  blooms  to  be  used  for  this  purpose  shall  have  at  least 
three  times  the  sectional  area  of  the  finished  pins. 

"All  pins  shall  be  accurately  turned  to  a  gauge,  and  shall  be  straight  and  smooth. 

"  The  clearance  between  pin  and  pin-hole  shall  be  J%  of  an  inch  for  all  lateral  pins  ; 
and  for  truss  pins  the  clearance  shall  be  ^  of  an  inch  for  pins  y/2  inches  in  diameter, 
which  amount  shall  be  gradually  increased  to  ?V  of  an  inch  for  pins  6  inches  in  diameter 
and  over.  . 

"  All  pins  shall  be  supplied  with  steel  pilot  nuts,  for  use  during  erection. 

"  All  pin-holes  shall  be  reenforced  by  additional  material  when  necessary,  so  as  not  to 
exceed  the  allowed  pressure  on  the  pins.  These  reenforcing  plates  must  contain  enough 
rivets  to  transfer  the  proportion  of  pressure  which  comes  upon  them,  and  at  least  one 
plate  on  each  side  shall  extend  not  less  than  6  inches  beyond  the  edge  of  the  tie  plate. 

"  Pin-holes  shall  be  bored  truly  parallel  with  one  another  and  at  right  angles  to  the 
axis  of  the  member  unless  otherwise  shown  in  drawings  ;  and  in  pieces  not  adjustable 
for  length,  no  variation  of  more  than  -fa  of  an  inch  for  every  20  feet  will  be  allowed  in 
the  length  between  centres  of  pin-holes. 

The  permissible  shearing  strain  and  bearing  pressure  are  given 
on  page  226. 

"  The  bending  strain  on  the  extreme  fibre  of  pins  shall  not  exceed  22,000  pounds  per 
square  inch  for  soft  steel  and  25,000  per  square  inch  for  medium  steel,  when  centres  of 
bearings  of  the  strained  members  are  taken  as  the  points  of  application  of  the  strains. 

TABLE  LXXVI. 

PINS  WITH  COTTERS. 

(AMERICAN  BRIDGE  Co.) 


Pin. 

Head. 

Cotter. 

Add  to  Grip. 

Diam 
of  Pin. 
P 

Diam  of 
Pin-Hole. 

at  End, 

Diam. 
H 

Thick- 
ness, 
T 

Length, 

Diam. 
D 

For  Length 
over  All, 
M 

For  Length 
under  Head, 

I" 

if 

¥  ?" 

¥     V 

\H 

! 

* 

If" 

\ 

l// 

! 

i 

2 

$ 

] 

! 

i 

3 

I 

2| 

in 

! 

V 

A 

I 

4 

5| 

3 

\ 

3i 

5 

I 

3  A 

III 

\ 

:  i! 

s! 

6 

2; 

2 

i 

NOTE.  —  Use  pins 

with  Lomas  nuts  in  preference  to  cotter  pins  whenever  possible. 

284 


MACHINE   DESIGN. 


TABLE  LXXVII. 

EYEBARS.* 
(AMERICAN  BRIDGE  Co.) 


Oxo. 


Width 

Mi 

D. 

He 

id. 

Screv 

rEnd. 

Min. 

oi 
Bar. 

0 

Ba 

r 
r. 

Diam 

. 

Ma 
Pi 

K. 
1, 

Additional  Mat. 
for  Head. 

Additional  Mat. 
for  Upset. 

Diam. 

length. 

Thicknesi 
of  Bar. 

3 

9J 

4 

L 

1 

8 

i 

4 

3 

6 

I 

4 

5 

10 

8 

3f 

6J 

IT35 

H^ 

4 

9 

9 

3t 

6J 

I 

5 

'      3 

1 

: 
\ 

"' 

5- 

s 

I 
ii 

9 
ii 

3| 

7 
8 

;i 

i 

r 

14^ 

6J 

2 

ii 

4 

8 

f 

16 

6 

3 

3 

4* 

9 

7 

H 

17 

7 

8 

3 

a 

9 

! 

c 

17 

b 

3 

8 

3 

t 

18 
i8J 

r 

7i 

10 

*NOTE. — Eye-bars  are  hydraulic  forged,  and  will  develop  the  full  strength  of  the  bar, 
under  conditions  given  in  the  above  table,  when  tested  to  destruction.  The  maximum 
sizes  of  pins  given  in  the  above  table  allow  an  excess  in  sectional  area  of  head  on  lines 
"  SS  "  over  that  of  the  body  of  the  bar  of  33  per  cent,  for  diameter  of  pins,  not  larger 
than  the  width  of  the  bar  and  36  per  cent,  for  pins  of  larger  diameter  than  the  width 
of  the  bar. 

"  Full  size  test  of  steel  eye-bars  shall  be  required  to  show  not  less  than  10  per  cent, 
elongation  in  the  body  of  the  bar,  and  tensile  strength  not  more  than  5,000  pounds 
below  the  minimum  tensile  strength  required  in  specimen  tests  of  the  grade  of  steel  from 
which  they  are  rolled.  The  bars  will  be  required  to  break  in  the  body,  but  should  a 
bar  break  in  the  head,  but  develop  10  per  cent,  elongation  and  the  ultimate  strength 
specified,  it  shall  not  be  cause  for  rejection,  provided  not  more  than  one  third  of  the 
total  number  of  bars  tested  break  in  the  head  ;  otherwise  the  entire  lot  will  be  rejected. 

"  The  heads  of  eye-bars  shall  not  be  less  in  strength  than  the  body  of  the  bar. 

"The  heads  of  eye-bars  shall  be  made  by  upsetting,  rolling,  or  forging  into  shape. 
Welds  in  the  body  of  the  bar  will  not  be  allowed. 

"The  bars  must  be  perfectly  straight  before  boring. 

"  The  holes  shall  be  in  the  centre  of  the  head  and  on  the  centre  line  of  the  bar. 

"  All  eye-bars  shall  be  annealed. 

' '  Bars  which  are  to  be  placed  side  by  side  in  the  structure  shall  be  bored  at  the  same 
temperature,  and  shall  be  of  such  equal  length  that,  upon  being  piled  on  each  other, 
the  pins  shall  pass  through  the  holes  at  both  ends  at  the  same  time  without  driving. ' ' 


APPENDIX.  285 


APPENDIX. 

PAGE  20.  In  many  shops,  a  custom  —  and  a  good  one  —  obtains 
of  covering  the  exposed  parts  of  shafts  of  twin-screw  steamers 
with  ratline  laid  in  paint,  when  the  shafts  are  not  cased  with  brass. 

The  use  of  pins  or  tap-rivets  as  an  aid  in  holding  shaft  casings 
does  not  meet  with  universal  approval,  the  argument  against  them 
being  that,  if  the  shrinkage  of  the  casing  does  not  fully  secure  the 
latter,  no  pins  will  ;  and,  further,  that  often  the  putting  in  of  the 
pins  tends  to  loosen  the  casing. 

PAGE  34.     The  expression, 


is  simply  the  value  of  Pl  obtained  from  the  third  equation  of  (27) 
by  making  P0,  in  that  equation,  equal  to  zero. 

PAGE  260.  The  "  Flat  Key"  is  the  type  used  almost  exclusively 
in  marine  work. 


INDEX. 


Bach,  experiments  on  joint  friction,  187 

lap-riveting,  181 

length  of  rivet-shank,  189 

riveting  temperature,  188 
Bands,  thin,  shrinkage  formulae,  3 
Boiler-braces,  275 

seams,    longitudinal,    circumferential, 

helical,  139 
Bolt-blanks,  no 

-heads,  stresses,  51 

heading  and  forging  machine,  1 10 

heads,  manufacturers'  standard,  53 

-threads,  cold-rolling  process,  114 
Bolts  and  nuts,  U.  S.  Standard  (Sellers),  50 
U.  S.  Navy,  52 
Whitworth,  55 

rods  for,  U.    S.   Naval  Specifications, 
114 

stresses,  71 
Braces,  boiler,  275 

tests,  277 

Calking,  effect  on  joint-friction,  190 
Cone-coupling,  Sellers,  255 
Cotters,  bolted  strap  end,  268 

connecting  rod,  267 

crosshead,  266 

driving  force,  272 

forms,  265 

friction,  273 

maximum  taper,  273 

piston,  265 

pump-rod,  266 

split-pins,  283 

stresses,  270 

taper-pins,  268 
Crank-shaft,  22 
Cylinders,   thick,    shrinkage  and   pressure 

formulae,  4 

Dies,  135 

Drilled  holes,  136 

Drilling  vs.  punching,  tests,  137,  138 


Engines,  marine,  19,  22,  23 

shrinkage     and     pressure 

joints,  19,  23 
keys,  260 
stationary,  259 
keys,  260 

Eye-bars,  proportions,  281,  284 
specifications,  281 
stresses,  277 
tests,  277 

Friction,  calking,  effect  on,  190 

coefficients  of,  9,  13,  87 

cotters,  273 

keys,  254,  264 

of  riveted  joints,  187 

of  support,  screws,  89 

plate,  130 

rivet-heads,  130 

screw,  82 

-threads,  44,  57,  82,  87,  89 
Furnace,  shrinkage,  39 

Gib  and  key,  267 

Grooved  ' '  specimens,  75 
Gun,  breech-block,  67 
-construction,  36 

shrinkage  in,  27 

expansion,  shrinkage,  clearance, 

41 

i6-in.  B.  L.  R.,  U.  S.  A.,  36 
radii  of  cylinders,  35 
relative  shrinkages  32 
shrinkage  formulae,  29 
-furnace,  39 
-pit,  40 
Stockett  system,  breech-mechanism,  38 

Heading  and  forging  machine,  1 10 
Hull-work,  Am.  Bureau  of  Shipping,  245 
laps  and  straps,  243 
plating,  thickness,  246 
proportions  of  seams,  239,  247 
punching,  drilling,  riveting,  245 


287 


288 


INDEX. 


Hull-work,  rivet-metals,  238 
riveted  joints,  235 
rivets,  proportions,  237,  241,  242 
spacing  of  rivets,  244 
U.  S.  Naval  practice,  237 

Key,  gib  and,  267 
Keys,  Blanton  fastening,  255 
cone,  255 
crushing  stress,  262 

feather,  252,  257 

flat,  252,  257 

forms,  251 

friction,  254 

Kernaul,  254 

machine-tools,  258 

marine  engine  work,  260 

on  the  flat,  256 

Peters  system,  253 

pin-,  254 

propeller-,  261 

proportions,  257 

quartering,  253 

roller,  255 

saddle,  254 

shafting,  258 

shearing  stress,  262 

square,  251,  257 

stationary  engine  work,  259 

stresses  on,  261 
from,  265 

sunk,  251 

through,  see  "Cotters" 

Woodruff,  253 
Key-ways,  milling  cutters,  259 

Nuts,  blanks,  1 12 

bursting  stress,  94 

circular,  52 

check,  118 

cold-punched,  112 

collar,  121 

elastic,  1 20 

forgings,  U.  S.  N.,  116 

hot-pressed,  manufacturers'   standard 

S3 

lock-plates,  123 
locks,  118 

Excelsior  double,  123 

Harvey  grip,  121 


^uts,  locks,  Jones  tie-bar,  123 

self-locking  threads,  121,  122 

set  screws,  120 

split  pins,  1 23 

Verona,  122 
Lomas,  282 

materials,  U.S.N.,  114,  116 
methods  of  manufacture,  1 1 2 
round,  slotted,  54 
self- locking,  121 
Sellers  system,  5 1 
stresses,  46,  51,  94 
tapping  machine,  114 
threading  and  tapping,  1 12 
washers,  national  lock,  122 

spring,  122 
Wiles  lock,  120 

Pin-joints,  274 

Pins,  bending  moment,  280 

stress,  276,  278 
proportions,  281,  282,  283 
shearing  stress,  276,  280 
split,  268,  283 
structural  work,  278 
taper,  268 

with  Lomas  nuts,  282 
Pipe,  spiral  riveted,  141 

-threads,  Briggs'  standard,  71 
Pit,  shrinkage,  40 

Plate,  boiler,  132,  207,  210,  215,  216 
flange,  229 

ship,  131,  237,  242,  246,  250 
structural,  131 
web,  231 
girder,  226 

perforated,  tensile  strength,  134 
Pressure  joints  (press  fits),  B.    F.  Sturte- 

vant  Co.,  17 
Buffalo  Forge  Co.,  18 
character  of  surfaces,  13 
coefficients  of  friction,  13 
forcing  pressure,  8,  13 
form,  12,  24 

Lane  and  Bodley  Co. ,  1 7 
length,  10 

marine  engines,  19,  23 
metals,  12 
proportions,  9 
railway  work,  24 


INDEX. 


289 


Pressure  joints  (press  fits),  resistance   to 

slip,  8 

Russell  Engine  Co.,  17 
slip-resistance    vs.     rotating 

force,  9 

stationary  engines,  16 
stresses   and   allowances,    6, 

10,  24 

summary  of  practice,  19 
thick  cylinders,  4,  6 
thickness,  II 

of  hub,  8 
wheel  fits,  25 
press,  25 
Punches,  135 
Punching,  effect  of,  136 
vs.  drilling,  137 

Railway-work,  shrink  and  press  fits,  24 
Riveted  joints,  Am.  Boiler  M'fr's  Asso'n, 

215 

Baldwin  Locomotive  Works,  210 
bearing  pressure,  157 
bending  stress,  185 
boilers,  percentage  strength  of,  172 
butt,  152,  161,  164,  190,  192 

efficiencies,  163 

straps,  173,  175 

unequal  straps,  153,  164 
elements,  142 
forms,  141 
friction,  187 
general  formulae,  170 
Hartford  Steam  Boiler  Insp.  and 

Ins.  Co.,  216 
hulls,  235 

lap,  154,  156,  I58>  '59,  i&>,  166 
laps  and  straps,  243 
location,  205,  213,  249 
locomotive  boilers,  210 
manner  of  failure,  143 
marine  boilers,  205 
plates,  stresses  upon,  186 

bending  stress,  185 

of  unequal  thickness,  176 
proportions,  207,  211 

of  seams,  239 
punching  vs.  drilling,  138 
U.  S.    Board  of  Supervising  In- 
spectors, 209 


Riveted  joints,  shearing  strength,  134 

stationary  boilers,  215 

theoretical  strength,  154 

stresses,  171,  178 

structural  work,  219 

tests,  192 

U.  S.  N.  practice,  237 
Riveted  members,  stresses  in,  224 
Riveter,  hydraulic,  202 

pneumatic,  203 

Riveting,  chain  and  staggered,  151,  174 
group,  154,  1 68 

hand,  frictional  resistance  in,  131 
hydraulic,  202 
machine,  190 
machines,  200,  202 
multiple,  146 
pneumatic,  202 
punching  and  riveting,  223 
spacing,  221 
structural,  231 
temperature,  187 
U.  S.  N.  specifications,  245 
Rivets,  American  Iron  and  Steel  Manufac- 
turing Company,  1 28 
bearing  value,  25 
blanks,  128 

diameter,  145,  172,  207,  219,  237,  242 
heads,   127,  128,  129,  207,  2U,  215, 

220,  237,  241 

holes,  134,  136,  138,  142,  215 
margin  and  lap,  149 
metals,    114,    131,     206,    210,    219, 

236,  237 

number  of  rows,  189 
proportions,  127,  207,  219,  237 
pitch,  147,  149,  172,  173 

diagonal,  147,  173 

transverse,  143,  149 
points,  127,  220,  237,  241 
shank,  130,  188 
bearing  stress,  185 
bending  stress,  181 
shearing  stress,  182 
tensile  stress,  180 
Victor,  128,  132 
weight,  209 

Screw-bolts,  armor,  66,  109 

combined  stresses  upon,  90,  IO2 


290 


INDEX. 


Screw-bolts,  cross-shear,  91 

efficiency,  101 

eye,  106 

friction  of  support,  89 

as  grooved  specimens,  75 

heading  machine,  no 

loss  of  axial  strength,  99 

methods  of  manufacture,  no 

materials,  114,  117 

resilience,  57,  81 

safe  loads,  103 

shaft-couplings,  91 

stay,  1 06,  1 08,  117 

studs,  104 

tap,  103,  104,  105 

tension,  static,  74 

sudden  load  or  impact,  79 

threading,  112 
tool,  113 

types,  103 
Screws,  geometry  of,  42 

machine,  68 

wood,  68 

set,  104,  105,  120 
Screw-threads,  bearing  pressure,  73 
surface,  56 

Briggs',  71 

Bristol  Association  Standard,  59 
buttress,  65 

.-old-pressed,  78 

density  of,  78 

diameter,  51 

durability,  57 

elements  of,  45 

forms,  43,  46,  51 

French  standard,  57 

friction  of,  44,  57,  82,  87,  89 

friction,  coefficients  of,  87 

international  Standard,  59 

interrupted,  67 

knuckle,  65 

lubricants,  87 

modified  triangular,  67 

multiple,  47 

pitch,  46,  51 

reinforcing  action  of,  75 

requirements,  45 

rupture,  72 

sharp  V,  54 

special,  65 


Screw-threads,  square,  6 1 

Newport  News  S.  B.  and  D.  D. 

Co.,  62 
Sellers,   61 
strength,  44,  56 
stress-ratio,  73 
stripping,  56,  72 
Swiss  system,  59 
tensile  strength,  56 
tests,  87 
torsion,  83 

triangular  vs.  square,  44 
U.  S.  Standard  (Sellers),  47 

modified,  51 

V,  Sellers,  Whitworth,  compared,  56 
#-V,  62 

Acme  standard,  64 

Newport  News  S.  B.  and  D.  D. 

Co.,  64 
Sellers,  63 
Whitworth,  55 
Sellers  thread,  47 
Shaft-casings,  20,  22,  24 

-couplings,   91 
Shafts,  marine  engine,  22 
Shell-sheets,  thickness,  177 
Shrinkage,  formulae,  guns,  29,  41 
thick  cylinders,  4 
thin  bands,  3 

guns,  radii  of  cylinders,  35 
in  gun  construction,  27 
stresses  and  strains,  guns,  30 
vs.  pressure  fits,  Wilmore,  15 
tires,  25 
Shrinkage  joints    (fits),    B.   F.   Sturtevant 

Co.,  1 8 

Buffalo  Forge  Co.,  18 
form,  12,  24 
length,  10 
marine  engines,  19,  22,  23 

crank-shafts,  22 
metals,  12 

Midvale  Steel  Company,  22 
proportions,  9 
railway  work,  24 
resistance  to  slip,  8 
Russell  Engine  Company,  17 
shaft-casings,  20,  22,  24 
slip-resistance     vs.     rotating 
force,  9,  15 


INDEX. 


29I 


Shrinkage  joints  (fits),  stresses  and  allow- 
ances, 6,  10,  24 
summary  of  practice,  19 
thickness,  8,  n 
thin  bands,  3 
tires,  25 

Union  Iron  Works,  23 
Shrinkages,  relative,  guns,  32 
Steel,  American  standard  specifications,  131 
boiler,  132,  194,  195,  215 
bolts,  114 
bridge,  131 
nuts,  116 
rivet,    114,    132,   206,  210,  219,  237 

238 

ship,  131,  237 
structural,  131,  219 
Stiffeners,  web,  231,  233 
Stresses  and  allowances,  6,  10,  24 

strains,  guns,  30 
bolt-heads,  51 
bolts,  71 

bursting,  nuts,  94 
cotters,  270 
eye-bars,  277 
from  keys,  263 
in  riveting,  168 
nuts,  46,  5 1 ,  94 
on  keys,  261 


Stresses  on  keys,  plates,  185 
riveted  joints,  171,  178 

members,  224 
rivets,  180,  181,  182,  183 
screw-threads,  73 
Structural  work,  bolts,  234 

distribution  of  stresses,  226 
flange-area,  angles,   flange-plates, 

229 

moments,  vertical   shear,   flange- 
stress,  228 
riveting,  231 
Stiffeners,  231,  233 
web-plate,  231 
Studs,  103 

cylinder-head,  92,  94 
metal,  U.  S.  N.,  114 

Temperature,  riveting,  187 

shrinkage,  14 
Tires,  shrinkage,  25 

Washers,  122 
Web-plates,  231 
Whitworth  thread,  55 
Wheel-fits,  25 

press,  25 

tires,  25 

Wood  screws,  68 
Wrenches,  loo,  124,  12$ 


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CLEVENGER,   S.   R.    A  Treatise  on  the  Method  of 

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CORNWALL,  Prof.  H.  B.  Manual  of  Blow-pipe  An- 
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COWELL,    W.  B.      Pure   Air,   Ozone   and  Water;    a 

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CRAIG,  B.  F.    Weights  and  Measures.    An  account  of 

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CROCKER,  F.  B.  Electric  Lighting.  A  Practical  Ex- 
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SCIENTIFIC  PUBLICATIONS.  11 


CROCKER,  F.  B.,  and  S.  S.  WHEELER.  The  Practical 

Management  of  Dynamos  and  Motors.  Fifth  Edition,  (Eleventh 
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Foster.  12mo,  cloth,  illustrated $1.00 

DAVIES,  E.  H.      Machinery  for  Metalliferous  Mines. 

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-  D.  C.     A  Treatise  on  Metalliferous  Minerals  and 

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MINING  MACHINERY In  Press. 

DAY,  CHARLES.     The  Indicator  and  its  Diagrams. 

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DENNY,  G.  A.     Deep-level  Mines  of  the  Rand,  and 

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DERR,  W.   L.    Block  Signal  Operation.    A  Practical 

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DIXON,  D.  B.      The  Machinist's  and  Steam  Engineer's 

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DODD,   GEO.     Dictionary  of  Manufactures,  Mining, 

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DORR,  B.  F.    The  Surveyor's  Guide  and  Pocket  Table 

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DRAPER,  C.  H.    An  Elementary  Text  Book  of  Light, 

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—  Cyanide  Process  for  the  Extraction  of  Gold  and  its 

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A  Hand-book  on  Modern  Explosives,  being  a  Prac- 
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SCIENTIFIC  PUBLICATIONS.  13 

ELIOT,  C.  W.,  and  STORER,  F.  H.    A  Compendious 

Manual  of  Qualitative  Chemical  Analysis.  Revised  with  the  co-oper- 
ation of  the  authors,  by  Prof.  William  R.  Nichols.  Illustrated. 
Twentieth  Edition,  newly  revised  by  Prof.  W.  B.  Lindsaij. 
12mo,  cloth net  $1.25 

ELLIOT,  Maj.  GEO..  H.  European  Light-House  Sys- 
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engravings  and  21  woodcuts.  8vo,  cloth  $5.00 

ELLISON,    LEWIS   M.     Practical  Application  of  the 

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styles  of  Engines.  Second  Edition,  revised.  8vo,  cloth,  100  illus- 
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ERFURT,  JULIUS.  Dyeing  of  Paper  Pulp ;  a  practi- 
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EVERETT,  J.  D.     Elementary  Text-Book  of  Physics. 

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FAIRIE,  JAMES,  F.  G.  S.    Notes  on  Lead  Ores ;  their 

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FANNING,  J.  T.      A  Practical  Treatise  on  Hydraulic 

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FISH,  J.  C.  L.  Lettering  of  Working  Drawings.  Thir- 
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FISKE,  Lieut.  BRADLEY  A.,  U.S.N.     Electricity  in 

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FLEMING,  Prof.  J.  A.  The  Alternate  Current  Trans- 
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Centenary    of  the  Electrical  Current,  1799-1899. 

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FOSTER,  Gen.  J.  G.,  U.S.A.      Submarine  Blasting  in 

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FOSTER,  H.  A.      Electrical  Engineers'  Pocket  Book. 

With  the  Collaboration  of  Eminent  Specialists.  A  handbook  of  use- 
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tables,  diagrams  and  figures.  Second  edition,  revised.  Pocket  size, 
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FOSTER,   JAMES.      Treatise  on  the  Evaporation  of 

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FOX,  WM.,  and  C.  W.  THOMAS,  M.  E.    A  Practical 

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SCIENTIFIC  PUBLICATIONS.  15 


FRANCIS,  Jas.  B.,  C.E.  Lowell  Hydraulic  Experi- 
ments. Being  a  selection  from  experiments  on  Hydraulic  Motors, 
on  the  Flow  of  Water  over  Weirs,  in  open  Canals  of  uniform  rec- 
tangular section,  and  through  submerged  Orifices  and  diverging 
Tubes.  Made  at  Lowell,  Mass.  Fourth  edition,  revised  and 
enlarged,  with  many  new  experiments,  and  illustrated  with  23 
copper- plate  engravings.  4to,  cloth $15.00 

FROST,  GEO.  H.    Engineer's  Field  Book.      By  C.   S. 

Cross.  To  which  are  added  seven  chapters  on  Railroad  Location  and 
Construction.  Fourth  edition.  l'2mo,  cloth $1.00 

FULLER,  GEORGE  W.    Report  on  the  Investigations 

into  the  Purification  of  the  Ohio  Kiver  Water  at  Louisville,  Ken- 
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Company.  Published  under  agreement  with  the  Directors.  3  full 
page  plates.  4to,  cloth net,  $10.00 

GARCKE,  EMILE,  and  J.  M.  FELLS.  Factory  Ac- 
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ings. Entirely  new  and  revised  edition.  8vo,  cloth,  illus../«  Press. 

GEIPEL,  WM.  and  KILGOUR,  M.  H.    A  Pocketbook 

of  Electrical  Engineering  Formulae.     Illustrated.     18mo,  mor.  .$3.00 

GERBER,  NICHOLAS.     Chemical  and  Physical  An- 

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GERHARD,  WM.  P.      Sanitary  Engineering.      12mo, 

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GESCHWIND,  LUCIEN.     Manufacture  of  Alum  and 

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ter.  With  tables,  figures  and  diagrams.  8vo,  cloth,  illus..  .net.  $5.00 

GIBBS,  WILLIAM  E.  Lighting  by  Acetylene,  Gen- 
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GILLMORE,  Gen.  Q.  A.    Treatise  on  Limes,  Hyraulic 

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Report  on  Strength  of  the  Building  Stones  in  the 

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GOLDING,    HENRY   A.      The    Theta-Phi    Diagram. 

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GOODEVE,  T.  M.     A  Text-Book  on  the  Steam-Engine. 

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143  illustrations.     12mo,  cloth '. $2.00 

GORE,  G.,  F.  R.  S.  The  Art  of  Electrolytic  Separa- 
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GOULD,  E.  SHERMAN.    The  Arithmetic  of  the  Steam 

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GROSS,  EMANUEL.  Hops,  in  their  Botanical,  Agri- 
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GROVER,  FREDERICK.  Practical  Treatise  on  Mod- 
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GRUNER,  ANTON.      Power-loom  Weaving  and  Yarn 

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GTJRDEN,    RICHARD    LLOYD.      Traverse    Tables: 

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GUY,  ARTHUR  F.     Electric  Light  and  Power,  giving 

the  Result  of  Practical  Experience  in  Central-Station  Work.  8vo, 
cloth.  Illustrated - $2.50 

HAEDER,   HERMAN,   C.  E.       A  Handbook    on   the 

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HALL,  WM.  S.   Prof.      Elements  of  the  Differential 

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Descriptive  Geometry,  with  numerous  Problems 

and  Practical  applications.     Two  vols .  (Plates  and  Text) ...In  Press. 


SCIENTIFIC  PUBLICATIONS.  17 


HALSEY,  F.   A.     Slide  Val^je  Gears,  an  Explanation 

of  the  action  and  Construction  of  Plain  and  Cut-off  Slide  Valves. 
Illustrated.  12mo,  cloth.  Seventh  Edition $1.50 

-  The  Use  of  the  Slide  Rule.    With  illustrations  and 

folding  plates.  Second  edition.  16mo,  boards.  ( Van  Nostrand's 
Science  Series,  No.  114.). $0.50 

The  Locomotive  Link  Motion,  with  Diagrams  and 

Tables.     8vo.  cloth,  illustrated $1.00 

Worm  and  Spiral  Gearing.      16mo,  cloth,  (Van  Nos- 
trand's Science  Series,  No.  116).     Illustrated $0.50 

HAMILTON,  W.  G.    Useful  Information  for  Railway 

Men.  Tenth  Edition,  revised  and  enlarged.  562  pages,  pocket 
form.  Morocco,  gilt $2.00 

HANCOCK,  HERBERT.    Text-Book  of  Mechanics  and 

Hydrostatics,  with  over  500  diagrams.      8vo,  cloth $1.75 

HARRISON,     W.    B.      The    Mechanics'    Tool    Book. 

With  Practical  Eules  and  Suggestions  for  use  of  Machinists,  Iron- 
Workers,  and  others.  Illustrated  with  44  engravings.'  12mo, 
cloth, $1.50 

HART,    JOHN    W.       External    Plumbing   Work;    a 

Treatise  on  Lead  Work  for  Roofs.  With  numerous  figures  and  dia- 
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—  Hints  to  Plumbers  on  Joint  Wiping,  Pipe  Bend- 
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Principles  of  Hot  Water  Supply.     With  numerous 

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H  AUFF,  W.  A.   American  Multiplier ;  Multiplications 

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HAUSNER,  A.    Manufacture  of  Preserved  Foods  and 

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HAWKINS,  C.  C.,  and  WALLIS,  F.      The  Dynamo ; 

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HAY,    ALFRED.      Principles    of  Alternate  -  Current 

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HEAVISIDE,    OLIVER.        Electromagnetic    Theory. 

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HERRMANN,    Gustav.      The    Graphical    Statics   of 

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HERMANN,  FELIX.  Painting  on  Glass  and  Porce- 
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HOFF,  WM.  B.,  Com.  TJ.  S.  Navy.    The  Avoidance  of 

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HOLMES,  A.  BROMLEY.  The  Electric  Light  Popu- 
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HOPKINS,  NEVIL  M.      Model   Engines    and    Small 

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HOSPITALLER,  E.    Polyphased  Alternating  Currents. 

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HOWORTH,  J.    Art  of  Repairing  and  Riveting  Glass, 

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HUMBER,  WILLIAM,  C.  E.    A  Handy  Book  for  the 

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HURST    GEO.  H.,  F.  C.  S.      Color;    a    Hand-book   of 

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HURST,  GEO.  H.,  F.  C.  S.    Lubricating  Oils,  Fats  and 

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HTJTTON,  W.  S.  Steam  Boiler  Construction.  A  Prac- 
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500  illustrations.  Third  Edition,  carefully  revised  and  much  en- 
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INNES,  CHARLES  H.  Problems  in  Machine  Design, 
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ISHERWOOD,  B.  F.  Engineering  Precedents  for  Steam 

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JAMESON,   CHARLES    D.      Portland  Cement.      Its 

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JAMIESON,  ANDREW,  C.E.    A  Text-Book  on  Steam 

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JANNETTAZ,  EDWARD.  A  Guide  to  the  Determina- 
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SCIENTIFIC  PUBLICATIONS.  21 


JEHL,  FRANCIS.  Member  A.  I.  E.  E.  The  manu- 
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numerous  diagrams,  tables  and  folding  plates.  8vo,  cloth,  illus- 
trated  84.00 

JENNISON,  FRANCIS  H.    The  Manufacture  of  Lake 

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different  processes  of  production.  8vo,  cloth,  illustrated  .  .net,  $3.00 

JOHNSTON,  Prof.  J.  F.  W.,  and  CAMERON,  Sir  Chas. 

Elements  of  Agricultural  Chemistry  and  Geology.  Seventeenth  Edi- 
tion. 12mo,  cloth $2.60 

JONES,  HARRY  C.      Outlines    of   Electrochemistry. 

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JONES,  M.  W.     The  Testing  and  Valuation  of  Raw 

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JOYNSON,  F.  H.      The  Metals  used  in  Construction. 

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Designing  and  Construction  of  Machine  Gearing. 

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KANSAS  CITY  BRIDGE,  THE     With  an  Account  of 

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KAPP,  GISBERT,  C.E.  Electric  Transmission  of  Ener- 
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Dynamos,  Motors,  Alternators  and  Rotary  Con- 
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KEMP,   JAMES  FURMAN,   A.   B.,  E.  M.      A  Hand- 

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KEMPE,  H.   R.     The    Electrical    Engineer's    Pocket 

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KENNELLY,  A.  E.  Theoretical  Elements  of  Electro- 
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KILGOUR,  M;  H.,  SWAN,  H.,  and  BIGGS,  C.  H.  W. 

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KING,  W.  H.    Lessons  and  Practical  Notes  on  Steam. 

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KINGDON,  J.  A.  Applied  Magnetism.  An  introduc- 
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KIRKALDY,   Wm.   G.    Illustrations  of  David  Kirk- 

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KIRKWOOD,   JAS.   P.     Report    on   the    Filtration  of 

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KNIGHT,  AUSTIN  M.,    (lieutenant- Commander   U.  S.  N.) 

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KOLLER,  THEODOR.  The  Utilization  of  Waste 
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LAMBERT,  THOMAS  Bone  Products  and  Manures: 

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LAMPRECHT,  ROBERT.    Recovery  Work  after  Pit 

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LARRABEE,  C.  S.  Cipher  and  Secret  Letter  and  Tele- 
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SCIENTIFIC  PUBLICATIONS.  23 


LASSAR-COHN,  Dr.    An  Introduction  to  Modern  Sci- 

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Pattison  Muir,  M.  A.  12mo,  cloth,  illustrated $2.00 

LEASK,  A.  RITCHIE.      Breakdowns  at  Sea  and  How 

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Refrigerating  Machinery :  Its  Principles  and  Man- 
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LECKY,  S.  T.  S.    "  Wrinkles  "  in  Practical  Navigation. 

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LEFEVRE,    LEON.      Architectural   Pottery:  Bricks, 

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and  W.  Moore  Binns.  4to,  cloth,  illustrated net  $7.50 

LEHNER,  SIGMUND.     Ink  Manufacture :    including 

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and  Herbert  Robson,  B.  Sc.  8vo,  cloth,  illustrated,  162  pages. 
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LEVY,   C.   L.     Electric  Light  Primer.    A  Simple  and 

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LIVACHE,  ACIL—(fnffenieur  Civil  De*  Mines.)  The  Man- 
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24  D.  VAN  NOSTRAND  COMPANY'S 

LOBBEN,  PEDER,  M.  E.    Machinists'  and  Draftsmen's 

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diagrams.  8vo,  cloth $2.50 

LOCKE,  ALFRED  G.  and  CHARLES  G.  A  Practical 
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LOCKERT,  LOUIS.  Petroleum  Motor-Car s.  12mo, 
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LOCKWOOD,  THOS.  D.  Electricity,  Magnetism,  and 
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—  Electrical  Measurement  and  the  Galvanometer ;  Its 

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LODGE,  OLIVER  J.    Elementary  Mechanics,  includ- 
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LODGE,  OLIVER  J.  Signalling  Across  Space,  With- 
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"With  numerous  diagrams  and  half  tone  cuts,  and  additional  remarks 
concerning  the  application  to  Telegraphy  and  later  developments. 
Third  edition.  8vo,  cloth,  illustrated net,  $2.00 

LORD,  R.  T.  Decorative  and  Fancy  Fabrics.  A  val- 
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signers of  Carpets,  i)amask,  Dress  and  all  Textile  Fabrics.  8vo, 
cloth,  illustrated net,  $3.50 

LORING,  A.  E.    A  Hand-Book  of  the  Electro-Magnetic 

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LUCE,   Com.   S.  B.      Text-Book  of  Seamanship.    The 

Equipping  and  Handling  of  Vessels  under  Sail  or  Steam.  For  the 
use  of  the  U.  S.  Naval  Academy.  Revised  and  enlarged  edition^ 
by  Lt.  Wm.  S.  Benson.  8vo,  cloth $10.00 

LUNGE,    GEORGE.    Ph.D.     Coal-Tar  and  Ammonia; 

being  the  third  and  enlarged  edition  of  "A  Treatise  on  the  Distilla- 
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A  Theoretical  and  Practical  Treatise  on  the  Man- 
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Vol.  I.  Sulphuric  Acid.  Second  Edition,  Revised  and  enlarged. 

342  illustrations.     8vo,  cloth $15.00 

Vol.  II.  Second  Edition,  revised  and  enlarged.  8vo,  cloth.  .$16.80 
Vol.  III.  8vo,  cloth.  New  Edition,  1896.. $15.00 


SCIENTIFIC  PUBLICATIONS.  25 


LUNGE,  GEO.,  and  HURTER,  F.    The  Alkali  Maker's 

Pocket  Book.  Tables  and  Analytical  Methods  for  Manufacturers  of 
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Edition.  12mo,  cloth $3.00 

LUQUER,  LEA  McILVAINE,   Ph.   D.      Minerals  in 

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Students  in  Technical  and  Sientific  Schools.  8vo,  cloth.  Illus- 
trated   net,  $1.50 

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Eccentric  upon  the  Slide- Valve,  and  explaining  the  practical  processed 
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MACKROW,  CLEMENT.    The  Naval  Architect's  and 

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MAGUIRE,  Capt.   EDWARD,  U.  S.  A.      The  Attack 

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MAGUIRE,  WM.   R.        Domestic  Sanitary  Drainage 

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MOREING,  C.  A.,  and  NEAL,  THOMAS.  New  Gen- 
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MOSES,  ALFRED  J.,  and  PARSONS,  C.  L.    Elements 

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MOSES,   ALFRED    J.      The  Characters  of  Crystals. 

An  Introduction  to  Physical  Crystallography,  containing  321  Illustra- 
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MTJLLIN,  JOSEPH  P.,  M.E.  '    Modern  Moulding  and 

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MUNRO,   JOHN,  C.E.,  and  JAMIESON,  ANDREW, 

C.  E.  A  Pocketbook  of  Electrical  Rules  and  Tables  for  the 
use  of  Electricians  and  Engineers.  Fifteenth  edition,  revised 
and  enlarged.  With  numerous  diagrams.  Pocket  size.  Leather.  $2.  50 

MURPHY,  J.  G.,  M.E.      Practical  Mining.     A  Field 

Manual  for  Mining  Engineers.  With  Hints  for  Investors  in  Mining 
Properties.  16mo,  morocco  tucks  ............................  $1.  00 

NAQTJET,  A.  Legal  Chemistry.   A  Guide  to  the  Detec- 

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and  Pharmaceutical  Substances,  Analysis  of  Ashes,  and  examination  of 
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preface  by  C.  F.  Chandler,  Ph.D.,  M.D.,  LL.D.  12mo,  cloth.  .82.00 

NASMITH,  JOSEPH,    The  Student's  Cotton  Spinning. 

Third  edition,  revised  and  enlarged.  8vo,  cloth,  622  pages,  250 
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NEUBTJRGER,   HENRY    and   HENRI  NOALHAT. 

Technology  of  Petroleum.     The  Oil  Fields  of  the  World  ;   their  His- 
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plates    Translated  from  the  French  by  John  Geddes  Mclntosh.    8vo, 
cloth,  'illustrated  ............................  '  ..........  nct>  S10-00 

N>EWALL,  JOHN  W.  Plain  Practical  Directions  for 
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may  be  eut  in  a  Plain  Milling  Machine  or  Gear  Cutter  so  as  to  give 
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NEWL.ANDS,  JAMES.    The  Carpenters'  and  Joiners' 

Assistant :  being  a  Comprehensive  Treatise  on  the  Selection,  Prepara- 
tion and  Strength  of  Materials,  and  the  Mechanical  Principles  of 
Framing,  with  their  application  in  Carpentry,  Joinery,  and  Hand- 
Railing  ;  also,  a  Complete  Treatise  on  Sines  ;  and  an  illustrated  Glos- 
sary of  Terms  used  in  Architecture  and  Building.  Illustrated.  Folio, 
half  morocco $15.00 

NTPHER,   FRANCIS  E.,  A.M.      Theory  of  Magnetic 

Measurements,  with  an  appendix  on  the  Method  of  Least  Squares. 
12mo,  cloth SI- 00 

NUGENT,  E.   Treatise  on  Optics;  or,  Light  and  Sight 

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O'CONNOR,   HENRY.      The  Gas   Engineer's    Pocket 

Book.  Comprising  Tables,  Notes  and  Memoranda;  relating  to  the 
Manufacture,  Distribution  and  Use  of  Coal  Gas  and  the  Construc- 
tion of  Gas  Works.  Second  edition,  revised.  12mo,  full  leather,  gilt 
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OSBORN,  FRANK  C.     Tables  of  Moments  of  Inertia, 

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OSTERBERG,  MAX.     Synopsis  of  Current  Electrical 

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OUDIN,  Maurice  A.      Standard  Polyphase  Apparatus 

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PAGE,  DAVID.  The  Earth's  Crust,  A  Handy  Out- 
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PALAZ,  A.,  ScD.  A  Treatise  on  Industrial  Photome- 
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revised.  8vo,  cloth.  Illustrated $4.00 

PARRY,  ERNEST  J.,  B.  Sc.  The  Chemistry  of  Essen- 
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PARRY,  LEONARD  A.,  M.  D.  The  Risks  and  Dan- 
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sanitary  inspectors,  medical  officers  of  health,  managers  of  works, 
foremen  and  workmen.  8vo,  cloth net.  $3.00 

PARSHALL,  H.  F.,  and  HOB  ART,  H.  M.     Armature 

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bles, and  165  pages  of  descriptive  letter-press.  4to,  cloth $7.50 

PARSHALL,  H.  F.,  and  EVAN  PARRY.     Electrical 

Equipment  of  Tramways {In  Press.) 

PATERSON,  DAVID,  F.  C.  S.     The  Color  Printing  of 

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PEIRCE,   B.      System    of  Analytic    Mechanics.    4to, 

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other  Uses ". /»  Press. 

PERRY,  JOHN.      Applied  Mechanics.      A  Treatise  for 

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PHILLIPS,    JOSHUA.      Engineering    Chemistry.     A 

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PICKWORTH,  CHAS.  N.     The  Indicator  Hand  Book. 

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tity with  High  Tension.  Translated  from  the  French  by  Paul  B. 
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PLATTNER'S  Manual  of  Qualitative  and  Quantitative 

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Morocco, $1.00 

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POPE,  F.  L.  Modern  Practice  of  the  Electric  Tele- 
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POPPLEWELL,  W.  C.    Elementary  Treatise  on  Heat 

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POWLES,   H.  H.     Steam  Boilers (In 


SCIENTIFIC  PUBLICATIONS.  31 


PRAY,  Jr.,  THOMAS.  Twenty  Years  with  the  In- 
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PREECE,  W.  H.    Electric  Lamps (In  Press.) 

PRELINI,  CHARLES.,  C.  E.  Tunneling;  a  Practical 

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PREECE,  W.  H.,  and  STUBBS,  A.  T.  Manual  of  Tele- 
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PRESCOTT,  Prof.  A.  B.    Organi9  Analysis.    A  Manual 

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PRITCHARD,  O.  G.  The  Manufacture  of  Electric 
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PULLEN,  W.  W.  F.     Application  of  Graphic  Methods 

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RANKINE,  W.  J.  MACQUORN.     Applied  Mechanics. 

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.  SCIENTIFIC  PUBLICATIONS.  35 


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SCIENTIFIC  PUBLICATIONS.  37 


SHIELDS,  J.  E.  Notes  on  Engineering  Construction. 

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STEWART,  R.  W.    A  Text  Book  of  Light.    Adapted 

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STILES,  AMOS.   Tables  for  Field  Engineers.   Designed 

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SCIENTIFIC  PUBLICATIONS. 


STONEY,  B.  D.    The  Theory  of  Stresses  in  Girders 

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STUART,  C.  B.  U.  S.  N.      Lives  and  Works  of  Civil 

and  Military  Engineers  of  America.  With  10  steel-plate  engravings. 
8vo,  cloth 85.00 

The    Naval   Dry  Docks  of  the  United    States. 

Illustrated  with  24  fine  Engravings  on  Steel.  Fourth  edition.  4to, 
cloth $6.00 

SUFFLING,    E.    R.      Treatise    on    the  Art  of  Glass 

Painting.  Prefaced  with  a  review  of  ancient  glass.  8vo,  cloth,  il- 
lustrated  net,  $3.50 

SWEET,  S.  H.     Special  Report  on  Coal,  showing  its 

Distribution,  Classification,  and  Costs  delivered  over  different  routes 
to  various  points  in  the  State  of  New  York  and  the  principal  cities  on 
the  Atlantic  Coast.  With  maps.  8vo,  cloth . . : $3.00 

SWINTON,  ALAN  A.  CAMPBELL.    The  Elementary 

Principle  of  Electric  Lighting.     Illustrated.     12mo,  cloth 60 

SWOOPE,  C.  WALTON.  Practical  Lessons  in  Elec- 
tricity ;  Principles,  Experiments  and  Arithmetical  Problems.  An 
Elementary  Text-Book.  With  numerous  tables,  formulae  and  two 
large  instruction  plates.  8vo,  cloth,  illustrated.  Third  edition. 
net,  $2.00 

TAILFER,  L.    Practical  Treatise  on  the  Bleaching  of 

Linen  and  Cotton  Yarn  and  Fabrics.  With  tables  and  diagrams. 
Translated  from  the  French  by  John  Geddes  Mclntosh.  8vo,  cloth, 
illustrated : $5.00 

TEMPLETON,  WM.  The  Practical  Mechanic's  Work- 
shop Companion.  Comprising  a  great  variety  of  the  most  useful 
rules  and  formulae  in  Mechanical  Science,  with  numerous  tables  of 
practical  data  and  calculated  results  facilitating  mechanical  operations. 
Ee vised  and  enlarged  by  W.  S.  Hutton.  12mo,  morocco $2.00 

THOM,  CHAS.,  and  WILLIS  H.  JONES.     Telegraphic 

Connections:  embracing  Recent  Methods  in  Quadruplex  Telegraphy. 
20  full  page  plates,  some  colored.  Oblong,  8vo,  cloth $1.50 

THOMPSON,  EDWARD  P.,  M.E.  How  to  Make  In- 
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for  Inventors.  Second  edition.  8vo,  boards $1.00 


40  D.  VAN  NOSTRAND  COMPANY'S 


THOMPSON,   EDWARD  P.,   M.   E.     Roentgen  Rays 

and  Phenomena  of  the  Anode  and  Cathode.  Principles,  Applications 
and  Theories.  For  Students,  Teachers,  Physicians,  Photographers, 
Electricians  and  others.  Assisted  by  Louis  M.  Pignolet,  N.  D.  C. 
Hodges,  and  Ludwig  Gutmann,  E.  E.  With  a  Chapter  on  Generali- 
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By  Professor  "Wm.  Anthony.  50  Diagrams,  40  Half-tones.  8vo, 
cloth $1.50 

THORNLEY,  T.      Cotton  Combing  Machines.     With 

numerous  tables,  engravings  and  diagrams.      8vo,  cloth,  illustrated. 

343  pages $3. 00 

Contents. — Preface,  List  of  Illustrations;  The  Silver  Lap  Ma- 
chine ;  Ribbon  Lap  Machine  and  Draw-Frame  ;  General  Description 
of  the  Heilmann  Comber ;  The  Cam  Shaft ;  The  Detaching  and  At- 
taching Mechanism  of  the  Comber ;  The  Duplex  Comber ;  Re-setting 
of  Combers  ;  The  erection  of  a  Heilmann  Comber ;  Stop  Motions  ; 
Various  Calculations  ;  Various  Notes  and  Discussions  ;  Cotton  Comb- 
ing Machines  of  Continental  Make  ;  Index. 

TODD,  JOHN  and  W.  B.  WHALL.  Practical  Seaman- 
ship for  Use  in  the  Merchant  Service  :  Including  all  ordinary  sub- 
jects ;  also  Steam  Seamanship,  Wreck  Lifting,  Avoiding  Collision, 
Wire  Splicing,  Displacement,  and  everything  necessary  to  be  known 
by  seamen  of  the  present  day.  Second  edition,  with  247  illustrations 
and  diagrams.  8vo,  cloth $8. 40 

TOOTHED  GEARING.       A  Practical  Hand-Book  for 

Offices  and  Workshops.  By  a  Foreman  Patternmaker.  184  Illustra- 
tions. 12mo,  cloth $2.25 

TRATMAN,   E.   E.   RUSSELL.     Railway  Track  and 

Track-Work.     With  over  two  hundred  illustrations.     8vo,  cloth. $3. 00 

TRAVERSE  TABLES,  showing  the  difference  of  Lati- 
tude and  Departure  for  distances  between  1  and  100,  and  for  angles  to 
quarter  degrees  between  1  degree  and  90  degrees.  Re-printed  from 
Scribner's  Pocket  Table  Book.  16mo,  boards.  (Van  Nostrand's 
/Science  Series.  No.  115) In  prefis. 

TRE VERT,  EDWARD.    How  to  build  Dynamo-Electric 

Machinery,  embracing  Theory  Designing  and  Construction  of  Dy- 
namos and  Motors.  With  appendices  on  Field  Magnet  and  Armature 
Winding,  Management  of  Dynamos  and  Motors,  and  Useful  Tables  of 
Wire  Gauges.  Illustrated.  8vo,  cloth $2.50 

Electricity  and  its  Recent  Applications.  A  Practi- 
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of  Electrical  Terms  and  Phrases.  Illustrated.  12mo,  cloth.  .$2.00 

TUCKER,  Dr.  J.  H.  A  Manual  of  Sugar  Analysis,  in- 
cluding the  Applications  in  General  of  Analytical  Methods  to  the 
Sugar  Industry.  With  an  Introduction  on  the  Chemistry  of  Cane 
Sugar,  Dextrose,  Levulose,  and  Milk  Sugar.  8vo,  cloth,  illus- 
trated  $3.50 


SCIENTIFIC  PUBLICATIONS. 


TTJMLIRZ,  Dr.  O.      Potential  and  its  Application  to 

the  Explanation  of  Electric  Phenomena,  Popularly  Treated.  Trans- 
lated from  the  German  by  D.  Robertson.  HI.  12mo,  cloth  ____  $1.25 

TTJNNER,  P.     A.    Treatise  on    Roll-Turning  for  the 

Manufacture  of  Iron.  Translated  and  adapted  by  John  B.  Pearse,  of 
the  Pennsylvania  Steel  Works,  with  numerous  engravings,  woodcuts. 
8vo,  cloth,  with  folio  atlas  of  plates  ..........................  $10.00 

URQTJHART,  J.  W.  Electric  Light  Fitting.    Embody- 

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Working  Electrical  Engineers.  With  numerous  illustrations.  12mo, 
cloth  .......................................................  $2.00 

-  Electro-Plating.     A   Practical  Hand  Book  on  the 

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ininum,  etc.  Third  edition.  12mo  ..........................  $2.00 

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and  Systematic  Guide  to  the  Reproduction  and  Multiplication  of 
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TJRQTJHART,  J.  W.     Dynamo  Construction  :  a  Practi- 

cal Hand-Book  for  the  Use  of  Engineer  Constructors  and  Electricians 
in  Charge,  embracing  Frame  Work  Building,  Field  Magnet  and  Arm- 
ature Winding  and  Grouping,  Compounding,  etc..  with  Examples  of 
Leading  English,  American  and  Continental  Dynamos  and  Motors, 
with  numerous  illustrations.  12mo,  cloth  ......................  $3.00 

-  Electric    Ship    Lighting.     A   Hand-Book  on   the 

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of  Ship  Owners  and  Builders,  Marine  Electricians  and  Sea  Going 
Engineers-  in-  Charge.  Numerous  illustrations.  12mo,  cloth  ......  $3.00 

UNIVERSAL    TELEGRAPH    CIPHER   CODE.    Ar- 

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VAN    NOSTRAND'S    Engineering    Magazine.     Com- 

plete sets,  1869  to  1886  inclusive. 

Complete  sets,  35  vols.  ,  in  cloth  ..............................  $60.00 

Complete  sets,  35  vols.  ,  in  half  morocco  .....................   100.00 


VAN  WAGENEN,  T.  F.  Manual  of  Hydraulic  . 

For  the  Use  of  the  Practical  Miner.  Hevised  and  enlarged  edition. 
18mo,  cloth  .................................................  $1.00 

VILLON,  A.  M.      Practical  Treatise  on  the  Leather 

Industry.  With  many  tables  and  illustrations  and  a  copious  index. 
A  translation  of  Villon's  "  Traite  Pratique  de  la  Fabrication  des 
Cuirs  et  du  Travail  des  Peaux,"  by  Frank  T.  Addyman,  B.  So.  8vo, 
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VINCENT,    CAMILLE.       Ammonia    and    its    Com- 

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by  M.  J.  Salter.  8vo,  cloth,  illustrated  ..........  •.  .  .  .....  net,  $2.00 


42  D.  VAN  NOSTRAND  COMPANY'S 


VON  GEORGIEVICS,  GEORG.    Chemical  Technology 

of  Textile  Fibres  ;    Their  Origin,  Structure,  Preparation,  Washing, 
Bleaching,   Dyeing,    Printing,  and   Dressing.     Translated  from  the 
German  by  Charles  Salter.      With  many  diagrams  and  figures.     8vo, 
cloth,  illustrated.     306  pages  .................................  $4.50 

Contents.  —  The  Textile  Fibres  ;  Washing,  Bleaching  and  Carbon- 
izing ;  Mordants  and  Mordanting  ;  Dyeing,  Printing,  Dressing  and 
Finishing  ;  Index. 

WALKER,  W.  H.     Screw  Propulsion.    Notes  on  Screw 

Propulsion,  its  Rise  and  History.     8vo,  cloth  ...................  75 

WALKER,   SYDNEY  F.      Electrical  Engineering  in 

Our  Homes  and  Workshops.  A  Practical  Treatise  on  Auxiliary  Elec- 
trical Apparatus.  Third  edition,  revised,  with  numerous  illustra- 
tions .......................................................  $2.00 

-  Electric  Lighting  for  Marine  Engineers,  or  How  to 

Light  a  Ship  by  the  Electric  Light  and  How  to  Keep  the  Apparatus 
in  Order.  103  illustrations.  8vo,  cloth.  Second  edition  .......  $2.00 

WALLIS-TAYLER,  A.  J.    Modern  Cycles,  A  Practi- 

cal Handbook  on  Their  Construction  and  Repair.  With  300  illustra- 
tions. 8vo,  cloth  ............................................  $4.00 

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-  Bearings  and  Lubrication.     A  Handbook  for  every 

user  of  Machinery.     Fully  illustrated.     8vo,  cloth  ..............  $1.50 

-    Refrigerating    and    Ice-Making    Machinery.       A 

Descriptive  Treatise  for  the  use  of  persons  employing  refrigerating 
and  ice-making  installations  and  others.  8vo,  cloth,  illustrated.  .  $3.  00 


pr 
36 


Refrigeration  and  Cold  Storage  ;  being  a  complete 

ractical  treatise  on  the  art  and  science  of  refrigeration.      600  pp., 
1  diagrams  and  figures.     8vo,  cloth,  illustrated  ..........  net,  $4.50 

-  Sugar  Machinery.    A  Descriptive  Treatise,  devoted 

to  the  Machinery  and  Apparatus  used  iu  the  Manufacture  of  Cane 
and  Beet  Sugars.     12mo,  cloth,  ill  ............................  $2.00 

WANKLYN,  J.  A.    A  Practical  Treatise  on  the  Exam- 

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WANSBROUGH,  WM.  D.    The  A.  B.  C.  of  the  Differ- 

ential Calculus.     12mo,  cloth  .................................  $1.50 

WARD,  J.  H.    Steam  for  the  Million.   A  Popular  Treat- 

ise on  Steam,  and  its  application  to  the  Useful  Arts,  especially  to 
Navigation.    8vo,  cloth  ....................................  $1.00 


SCIENTIFIC  PUBLICATIONS.  43 


WARING,  GKEO.  E.,  Jr.    Sewerage  and  Land  Drainage. 

Illustrated  with  wood-cuts  in  the  text,  and  full-page  and  folding 
plates.  Quarto.  Cloth.  Third  edition $6. 00 

Modern  Methods  of  Sewage  Disposal  for  Towns, 

Public  Institutions  and  Isolated  Houses.  Second  edition,  revised 
and  enlarged.  260  pages.  Illustrated,  cloth $2.00 

How  to  Drain  a  House.     Practical  Information  for 

Householders.     Third  edition  enlarged.     12mo,  cloth...       . . .   $1 .25 

WATSON,  E/PT^  Small  Engines  and  Boilers. ^A  man- 
ual of  Concise  and  Specific  Directions  for  the  Construction  of  Small 
Steam  Engines  and  Boilers  of  Modern  Types  from  five  Horse-power 
down  to  model  sizes.  Illustrated  with  Numerous  Diagrams  and  Half 
Tone  Cuts.  12mo,  cloth $1.25 

WATT,  ALEXANDER.  Electro-Deposition.  A  Prac- 
tical Treatise  on  the  Electrolysis  of  Gold,  Silver,  Copper,  Nickel,  and 
other  Metals,  with  Descriptions  of  Voltaic  Batteries,  Magneto  and 
Dynamo-Electric  Machines,  Thermopiles,  and  of  the  Materials  and 
Processes  used  in  every  Department  of  the  Art,  and  several  chapters 
on  Electro-Metallurgy.  With  numerous  illustrations.  Third  edition, 
revised  and  corrected.  New  and  enlarged  edition In  Press. 

Electro-Metallurgy  Practically  Treated.     Eleventh 

edition,  considerably  enlarged.     12mo,  cloth $1.00 

The  Art  of  Soap-Making.    A  Practical  Handbook 

of  the  Manufacture  of  Hard  and  Soft  Soaps,  Toilet  Soaps,  &c.  In- 
cluding many  New  Processes,  and  a  Chapter  on  the  Recovery  of 
Glycerine  from  Waste  Lyes.  With  illustrations.  Fifth  edition, 
revised  and  enlarged.  8vo,  cloth $3.00 

WATT,  ALEXANDER.  The  Art  of  Leather  Manufact- 
ure. Being  a  Practical  Handbook,  in  which  the  Operations  of  Tan- 
ning, Currying,  and  Leather  Dressing  are  Fully  Described,  and  the 
Principles  of  Tanning  Explained,  and  many  Recent  Processes  Intro- 
duced. With  numerous  illustrations.  Second  edition.  8vo,  cl.$4.00 

WE  ALE,  JOHN.     A  Dictionary    of  Terms  Used   in 

Architecture,  Building,  Engineering,  Mining,  Metallurgy,  Archaelogy, 
the  Fine  Arts,  etc. ,  with  explanatory  observations  connected  with 
applied  Science  and  Art.  fifth  edition,  revised  and  corrected. 
12mo,  cloth $2. 50 

WEBB,   HERBERT  LAWS.      A  Practical    Guide   to 

the  Testing  of  Insulated  Wires  and  Cables.  Illustrated.  12mo, 
cloth $1.00 

The  Telephone  Hand  Book.       128  illustrations.      146 

16mo.,   cloth. $1.00 


WEEKES,  R.   W.    The   Design  of  Alternate  Current 

Transformers.     Illustrated.     12mo,  cloth $1.00 


44  D.  VAN  NOSTKAND  COMPANY'S 


WEISBACH,    JULIUS.     A    Manual    of    Theoretical 

Mechanics.  Ninth  American  edition.  Translated  from  the  fourth 
augmented  and  improved  German  edition,  with  an  Introduction  to 
the  Calculus  by  Eckley  B.  Coxe,  A.M.,  Mining  Engineer.  1,100 

pages,  and  902  woodcut  illustrations.     8vo,  cloth $6.00 

Sheep 7.50 

WESTON,    EDMUND  B.      Tables    Showing   Loss  of 

Head  Due  to  Friction  of  Water  in  Pipes.  Second  edition.  12mo, 
cloth $1.50 

WEYMOUTH,   F.   MARTEN.      Drum  Armatures  and 

Commutators.  (Theory  and  Practice.)  A  complete  Treatise  on  the 
Theory  and  Construction  of  Drum  Winding,  and  of  commutators  for 
closed-coil  armatures,  together  with  a  full  resume  of  some  of  the  prin- 
cipal points  involved  in  their  design,  and  an  exposition  of  armature 
re-actions  and  sparking.  8vo,  cloth $3.00 

WHEELER,  Prof,  J.  B.      Art  of  War.      A  Course  of 

Instruction  in  the  Elements  of  the  Art  and  Science  of  War,  for  the 
Use  of  the  Cadets  of  the  United  States  Military  Academy,  West  Point, 
N.  Y.  12mo,  cloth SI. 75 

Field    Fortifications.      The    Elements    of  Field 

Fortifications,  for  the  Use  of  the  Cadets  of  the  United  States  Military 
Academy,  West  Point,  N.  Y.  12mo,  cloth $1.75 

WHIPPLE,   S.,  C.  E.      An  Elementary  and  Practical 

Treatise  on  Bridge  Building.      8vo,  cloth $3.00 

WHITE,  W.  H.,  K.  C.  B.  A  Manual  of  Naval  Archi- 
tecture, for  use  of  Officers  of  the  Royal  Navy,  Officers  of  the  Merchan- 
tile  Marine,  Yachtsmen,  Shipowners  and  {Shipbuilders.  Containing 
many  figures,  diagrams  and  tables.  Thick,  8vo,  cloth,  illus $9.00 

WILKINSON,  H.  D.  Submarine  Cable-Laying,  Re- 
pairing and  Testing.  8vo,  cloth $5.00 

WILLIAMSON,  R.  S.    On  the  Use  of  the  Barometer  on 

Surveys  and  Reconnoissances.  Part  L  Meteorology  in  its  Connection 
with  Hypsometry.  Part  II.  Barometric  Hypsometry.  With  Illus- 
trative tables  and  engravings.  4to,  cloth $15 .00 

Practical  Tables  in  Meteorology  and  Hypsometry, 

in  connection  with  the  use  of  the  Barometer.     4to,  cloth $2. 50 

WILSON,  GEO.  Inorganic  Chemistry,  with  New  No- 
tation. Revised  and  enlarged  by  H.  G.  Madan.  New  edition. 
12mo,  cloth $2.00 

WINKLER,  CLEMENS.    Handbook  of  Technical  Gas- 

Analysis.  With  figures  and  diagrams.  Second  English  Edition, 
Translated  from  the  Third,  greatly  enlarged  German  Edition,  with 
some  additions  by  George  Lunge,  Ph.  D.  8vo,  cloth,  illustrated,  190 
pages $4.00 


SCIENTIFIC  PUBLICATIONS.  45 


WOODBURY,  D.  V.    Treatise  on  the  Various  Elements 

of  Stability  in  the  Weil-Proportioned  Arch.    8vo,  half  morocco.. $4. 00 

WRIGHT,  T.  W.,  PROF.  (Union  College).  Elements  of 
Mechanics ;  including  Kinematics,  Kinetics  and  Statics.  With  ap- 
plications. Third  edition,  revised  and  enlarged.  8vo,  cloth . .  $2. 50 

WYLIE,  CLAUDE.  Iron  and  Steel  Founding.  Illus- 
trated with  39  diagrams.  Second  edition,  revised  and  enlarged. 
8vo,  cloth $2.00 

WYNKOOP,    RICHARD.      Vessels  and   Voyages,    as 

Regulated  by  Federal  Statutes  and  Treasury  Instructions  and  Decis- 
ions. 8vo,  cloth $2.00 

YOUNG,  J.  ELTON.      Electrical  Testing  for  Telegraph 

Engineers.  With  Appendices  consisting  of  Tables.  8vo,  cloth,  illus- 
trated  $4.00 

YOUNG     SEAMAN'S     MANUAL.       Compiled   from 

Various  Authorities,  and  Illustrated  with  Numerous  Original  and 
Select  Designs,  for  the  Use  of  the  United  States  Training  Ships  and 
the  Marine  Schools.  8vo,  half  roan $3.00 

ZIPSER,    JULIUS.       Textile    Raw    Materials,    and 

their  Conversion  into  Yarns.  The  study  of  the  Eaw  Materials  and 
the  Technology  of  the  Spinning  Process.  A  Text-book  for  Textile, 
Trade  and  higher  Technical  Schools,  as  also  for  self -instruction. 
Based  upon  the  ordinary  syllabus  and  curriculum  of  the  Imperial  and 
Royal  Weaving  Schools.  Translated  from  the  German  by  Chas.  Sal- 
ter.  8vo,  cloth,  illustrated $5.00 


Catalogue  of  the  Van  Nostrand 

Science  Series. 


*T*HEY  are  put  up  in  a  uniform,  neat,  and  attractive  form. 

•*•  boards.  Price  jo  cents  per  volume.  The  subjects  are  of  an 
eminently  scientific  eharacter,  and  embrace  a  wide  range  of  topics,  and 
are  amply  illustrated  when  the  subject  demands. 

No.  I.     CHIMNEYS  FOR  FURNACES  AND  STEAM-BOILERS. 

By  R.  Armstrong,  C.E.  Third  American  edition,  revised  and  partly 
rewritten,  with  an  appendix  on  Theory  of  Chimney  Draught,  by  F.  E. 
Well,  M.E. 

No.  2.  STEAM-BOILER  EXPLOSIONS.  By  Zerah  Colburn.  N«w 
edition,  revised  by  Prof.  R.  H.  Thurston. 

No.  3.     PRACTICAL    DESIGNING     OF     RETAINING- WALLS. 

By  Arthur  Jacob,  A.B.  Second  edition,  revised,  with  additions  by  Prof. 
W.  Cain. 

No.  4.  PROPORTIONS  OF  PINS  USED  IN  BRIDGES.  Second 
edition,  with  appendix.  By  Charles  E.  Bender,  C.E. 

No.  5.  VENTILATION  OF  BUILDINGS.  By  W.  F.  Butler.  Second 
edition,  re-edited  and  enlarged  by  James  L.  Greenleaf,  C.E. 

No.  6.     ON     THE     DESIGNING     AND      CONSTRUCTION      OF 

STORAGE  RESERVOIRS.  By  Arthur  Jacob,  A.B.  Second  edition, 
revised,  with  additions  by  E.  Sherman  Gould. 

No.  7.     SURCHARGED    AND    DIFFERENT    FORMS    OF     RE- 

TAINING-WALLS.     By  James  S.  Tate,  C.E. 

No.  8.  A  TREATISE  ON  THE  COMPOUND  ENGINE.  By  John 
Turnbull,  jun.  Second  edition,  revised  by  Prof.  S.  W.  Robinson. 

No.  9.  A  TREATISE  ON  FUEL.  By  Arthur  V.  Abbott,  C.  E. 
Founded  on  the  original  treatise  of  C.  William  Siemens,  D.C.L. 

No.  10.  COMPOUND  ENGINES.  Translated  from  the  French  of  A. 
Mallet.  Second  edition,  revised,  with  Results  of  American  Practice,  by 
Richard  H.  Buel,  C.E. 

No.  n.     THEORY  OF  ARCHES.     By  Prof.  W.  Allan. 

No.  12.     A    THEORY    OF    VOUSSOIR    ARCHES.     By  Prof.  W.  E. 

Cain.     Second  edition,  revised  and  enlarged.     Illustrated. 
No.  13.     GASES  MET  WITH  IN  COAL-MINES.     By  J.  J.  Atkinson. 

Third  edition,  revised  and  enlarged  by  Edward  H  Williams,  jun. 


D.   VAN  NOSTRAND  COMPANY'S 


No.  14.     FRICTION  OF  AIR  IN  MINES.     By  J.  J.  Atkinson. 

No.  15.     SKEW   ARCHES.     By  Prof.  E.  W.  Hyde,  C.E.     Illustrated 

No.  16.  A  GRAPHIC  METHOD  OF  SOLVING  CERTAIN  QUES- 
TIONS IN  ARITHMETIC  OR  ALGEBRA.  By  Prof.  Geo.  L.  Vose. 

No.  17.  WATER  AND  WATER-SUPPLY.  By  Prof.  W.  H.  Corfield 
of  the  University  College,  London. 

No.  18.  SEWERAGE  AND  SEWAGE  PURIFICATION.  By 
M.  N.  Baker,  Assoc.  Ed.  Engineering  News. 

No.  19.     STRENGTH     OF     BEAMS     UNDER     TRANSVERSE 

LOADS.    By  Prof.  W.  Allan,  author  of  "Theory  of  Arches." 

No.  20.  BRIDGE  AND  TUNNEL  CENTRES.  By  John  B.  Mc- 
Master,  C.E. 

No.  21.     SAFETY   VALVES.     By  Richard  H.  Buel,  C.E.  Third  edition. 
No.  22.     HIGH    MASONRY    DAMS.     By   E.  Sherman  Gould,  C.E. 

No.  23.  THE  FATIGUE  OF  METALS  UNDER  REPEATED 

STRAINS.  With  Various  Tables  of  Results  and  Experiments.  From 
the  German  of  Prof.  Ludwig  Spangenburgh,  with  a  Preface  by  S.  H. 
Shreve,  A.M. 

No.  24.  A  PRACTICAL  TREATISE  ON  THE  TEETH  OF 

WHEELS.     By  Prof.  S.  W.  Robinson.     Second  edition,  revised. 

No.  25.  ON  THE  THEORY  AND  CALCULATION  OF  CON- 
TINUOUS BRIDGES.  By  R.  M.  Wilcox,  Ph.B. 

No.  26.     PRACTICAL    TREATISE  ON    THE   PROPERTIES  OF 

CONTINUOUS    BRIDGES      By  Charles  Bender,  C.E. 

No.  27.     ON     BOILER     INCRUSTATION      AND     CORROSION 

By  F.  J.  Rowan.     New  edition,  revised  and  partly  rewritten  by  F.  L. 
Idell,  M.  E. 
No.  28.     TRANSMISSION      OF     POWER     BY     WIRE     ROPES 

By  Albert  W.  Stahl,  U.S.N.     Second  edition. 

No.  29.  STEAM  INJECTORS.  Translated  from  the  French  ol 
M.  Leon  Pochet. 

No.  30.  TERRESTRIAL  MAGNETISM,  AND  THE  MAGNET- 
ISM  OF  IRON  VESSELS.  By  Prof.  Fairman  Rogers. 

Wo.  31.      THE      SANITARY      CONDITION     OF      DWELLING- 

HOUSES   IN   TOWN  AND  COUNTRY.     By  George  E.  Waring,  jun, 

No.  32.  CABLE-MAKING  FOR  SUSPENSION  BRIDGES.  By 
W.  Hildenbrand,  C.E. 

No.  33.     MECHANICS   OF   VENTILATION.     By  George  W.  Rafter, 

C.E.     New  edition  (1895),  revised  by  author. 
No.  34.     FOUNDATIONS.      By  Prof.  Jules   Gaudard,  C.E.      Translated 

from  the  French. 

No.  35.  THE  ANEROID  BAROMETER:  ITS  CONSTRUC- 
TION AND  USE.  Compiled  by  George  W.  Plyfnpton.  Eighth  edition. 

No.  36.  MATTER  AND  MOTION.  By  J.  Clerk  Maxwell,  M.A. 
Second  American  edition. 


SCIENCE  SERIES. 


No.  37.     GEOGRAPHICAL    SURVEYING:    ITS    USES,    METH- 
ODS, AND  RESULTS.    By  Frank  De  Yeaux  Carpenter,  C.E. 

No.  38.    MAXIMUM    STRESSES    IN    FRAMED    BRIDGES.     By 
Prof.  William  Cain,  A.M.,  C.E.    New  and  revised  edition. 

No.  39.    A      HANDBOOK      OF      THE      ELECTRO-MAGNETIC 

TELEGRAPH.    By  A.  E.  Loring.    New  enlarged  edition. 
No.  40.     TRANSMISSION  OF  POWER  BY  COMPRESSED  AIR. 

By  Robert  Zahner,  M.E.    Second  edition. 
No.  41.     STRENGTH  OF  MATERIALS.    By  William  Kent,  C.E., 

Assoc.  Ed.  Engineering  News. 
No.  42.    THEORY    OF    STEEL-CONCRETE    ARCHES    AND 

OF  VAULTED  STRUCTURES.     By  Prof.  William  Cain. 
No.  43.     WAVE   AND  VORTEX   MOTION.     By  Dr.  Thomas  Craig  of 

Johns  Hopkins  University. 
No.  44.     TURBINE   WHEELS.     By  Prof.  W.  P.  Trowbridge,  Columbia 

College.     Second  edition. 
No.  45.     THERMODYNAMICS.     By  Prof.   H.  T.  Eddy,  University  of 

Cincinnati. 

No.  46.     ICE-MAKING   MACHINES.     New  edition,  revised  and  en- 
larged  by  Prof.  J.  E.  Denton.     From  the  French  of  M.  Le  Doux. 

No.  47.     LINKAGES;    THE    DIFFERENT   FORMS   AND  USES 
OF  ARTICULATED  LINKS.    By  J.  D.  C.  de  Roos. 

No.  48.     THEORY    OF     SOLID    AND    BRACED    ARCHES.      By 
William  Cain,  C.E. 

No.  49.     ON    THE    MOTION    OF    A    SOLID   IN    A    FLUID.     By 

Thomas  Craig,  Ph.D. 

No.  50.     DWELLING-HOUSES  :       THEIR      SANITARY      CON- 

STRUCTION   AND    ARRANGEMENTS.     By  Prof.  W.  H.  Corfield. 


51. 

Th 


omas  Nolan. 

No.  52.  IMAGINARY  QUANTITIES.  Translated  from  the  French  of 
M.  Argand.  By  Prof.  Hardy. 

No.  53.     INDUCTION  COILS  :   HOW  MADE  AND  HOW  USED. 

Third  American,  from  Ninth  English  edition. 

No.  54.  KINEMATICS  OF  MACHINERY.  By  Prof.  Kennedy.  With 
an  introduction  by  Prof.  R.  H.  Thurston. 

No.  55.     SEWER  GASES  :  THEIR  NATURE  AND  ORIGIN.     By 

A.  de  Varona. 

No.  56.  THE  ACTUAL  LATERAL  PRESSURE  OF  EARTH- 
WORK. By  Benjamin  Baker,  M.  Inst  C.E. 

No.  57.  INCANDESCENT  ELECTRIC  LIGHTING.  A  Practical 
Description  of  the  Edison  System.  By  L.  H.  Latimer,  to  which  is 
added  the  Design  and  Operation  of  Incandescent  Stations,  by  C.  J. 
Field,  and  the  Maximum  Efficiency  of  Incandescent  Lamps,  by  John 
W.  Howell. 

No.  58.  THE  VENTILATION  OF  COAL-MINES.  By  W.  Fairley. 
M.E  ,  F.S.S. 


D.   VAN  NO  STRAND  COMPANY'S 


No.  59.  RAILROAD  ECONOMICS;  OR,  NOTES,  WITH  COM- 
MENTS. By  S.  W.  Robinson,  C.E. 

No.  60.     STRENGTH    OF    WROUGHT  IRON     BRIDGE     MEM- 

BERS.     By  S.  W.  Robinson,  C.E. 

No.  61.  POTABLE  WATER  AND  METHODS  OF  DETECT- 
ING IMPURITIES.  By  M.  N.  Baker,  Ph.B. 

No.  62.  THE  THEORY  OF  THE  GAS-ENGiNE.  By  Dugald  Clerk. 
Second  edition.  With  additional  matter.  Edited  by  F.  E.  Idell,  M.E. 

No.  63.  HOUSE  DRAINAGE  AND  SANITARY  PLUMBING. 

By  W.  P.  Gerhard.     Eighth  edition,  revised. 

No.  64.     ELECTRO-MAGNETS.  By  A.  N.  Mansfield,  S.B. 

No.  65.  POCKET  LOGARITHMS  TO  FOUR  PLACES  OF  DECI- 
MALS. 

No.  66.  DYNAMO-ELECTRIC  MACHINERY.  By  S.  P.  Thompson 
With  notes  by  F.  L.  Pope.  Third  edition. 

No.  67.  HYDRAULIC  TABLES  BASED  ON  "KUTTER'S 
FORMULA."  By  P.  J.  Flynn. 

No.  68.  STEAM-HEATING.  By  Robert  Briggs.  Third  edition,  revised, 
with  additions  by  A.  R.  Wolff. 

No.  69.  CHEMICAL  PROBLEMS.  By  Prof.  J.  C.  Foye.  Fourth 
edition,  revised  and  enlarged. 

No.  70.  EXPLOSIVE  MATERIALS.  The  Phenomena  and  Theories 
of  Explosion,  and  the  Classification,  Constitution  and  Preparation  of 
Explosives.  By  First  Lieut.  John  P.  Wisser,  U.S.A. 

No.  71.  DYNAMIC  ELECTRICITY.  By  John  Hopkinson,  J.  N. 
Shoolbred,  and  R.  E.  Day. 

No.  72.  TOPOGRAPHICAL  SURVEYING.  By  George  J.  Specht, 
Prof.  A.  S.  Hardy,  John  B.  McMaster,  and  H.  F.  Walling. 

No.  73.  SYMBOLIC  ALGEBRA;   OR,  THE  ALGEBRA  OP 

ALGEBRAIC  NUMBERS.     By  Prof.  W.  Cain. 

No.  74.  TESTING  MACHINES  :  THEIR  HISTORY,  CON- 
STRUCTION, AND  USE.  By  Arthur  V.  Abbott. 

No.  75.  RECENT  PROGRESS  IN  DYNAMO-ELECTRIC  MA- 
CHINES. Being  a  Supplement  to  Dynamo-Electric  Machinery.  By 
Prof.  Sylvanus  P.  Thompson. 

No.  76.  MODERN  REPRODUCTIVE  GRAPHIC  PROCESSES. 

By  Lieut.  James  S.  Pettit,  U.S.A. 

No.  77.  STADIA  SURVEYING.  The  Theory  ot  Stadia  Measurements. 
By  Arthur  Winslow. 

No.  78.  THE  STEAM-ENGINE  INDICATOR,  AND  ITS  USE 
By  W.  B.  Le  Van. 

No.  79.     THE  FIGURE  OF  THE  EARTH.     By  Frank  C.  Roberts, C.E. 

No.  80.  HEALTHY  FOUNDATIONS  FOR  HOUSES.  By  Clew 
Brown- 


SCIENCE  SERIES. 


No.  81.     WATER      METERS  :       COMPARATIVE      TESTS     OF 

ACCURACY,  DELIVERY,   ETC.     Distinctive  features  of  the  Worth- 
ington,  Kennedy,  Siemens,  and  Hesse  meters.     By  Ross  E.  Browne. 

No.  82.  THE  PRESERVATION  OF  TIMBER  BY  THE  USE 
OF  ANTISEPTICS.  By  Samuel  Bagster  Boulton,  C.E. 

No.  83.  MECHANICAL  INTEGRATORS.  By  Prof.  Henry  S.  H. 
Shaw,  C.E. 

No.  84.  FLOW  OF  WATER  IN  OPEN  CHANNELS,  PIPES, 
CONDUITS,  SEWERS,  ETC.  With  Tables.  By  P.  J.  Flynn,  C.E. 

No.  85.     THE  LUMINIFEROUS  AETHER.     By  Prof,  de  Volson  Wood. 

No.  86.     HAND-BOOK  OF  MINERALOGY;  DETERMINATION 

AND  DESCRIPTION  OF  MINERALS  FOUND  IN  THE  UNITED 
STATES.     By  Prof.  J.  C.  Foye. 

No.  87.  TREATISE  ON  THE  THEORY  OF  THE  CON- 
STRUCTION OF  HELICOIDAL  OBLIQUE  ARCHES.  By  John 
L.  Culley,  C.E. 

No.  88.  BEAMS  AND  GIRDERS.  Practical  Formulas  for  their  Re- 
sistance.  By  P.  H.  Philbrick. 

No.  89.     MODERN       GUN-COTTON:      ITS      MANUFACTURE, 

PROPERTIES,  AND  ANALYSIS.     By  Lieut.  John  P.  Wisser,  U.S.A. 

No.  90.  ROTARY  MOTION,  AS  APPLIED  TO  THE  GYRO- 
SCOPE. By  Gen.  J.  G.  Barnard. 

No.  91.  LEVELING:  BAROMETRIC,  TRIGONOMETRIC,  AND 
SPIRIT.  By  Prof.  I.  O.  Baker. 

No.  92.     PETROLEUM  :     ITS     PRODUCTION     AND     USE.      By 

Boverton  Redwood,  F.I.C.,  F.C.S. 

No.  93.  RECENT  PRACTICE  IN  THE  SANITARY  DRAIN- 
AGE OF  BUILDINGS.  With  Memoranda  on  the  Cost  of  Plumbing 
Work.  Second  edition,  revised.  By  William  Paul  Gerhard,  C.  E. 

No.  94.  THE  TREATMENT  OF  SEWAGE.  By  Dr.  C.  Meymott 
Tidy. 

No.  95.  PLATE  GIRDER  CONSTRUCTION.  By  Isami  Hiroi,  C.E. 
Second  edition,  revised  and  enlarged.  Plates  and  Illustrations. 

NO.  96.  ALTERNATE  CURRENT  MACHINERY.  By  Gisbert 
Kapp,  Assoc.  M.  Inst.,  C.E. 

No.  97.     THE    DISPOSAL    OF    HOUSEHOLD   WASTE.     By  W. 

Paul  Gerhard,  Sanitary  Engineer. 

No.  98.  PRACTICAL  DYNAMO-BUILDING  FOR  AMATEURS. 
HOW  TO  WIND  FOR  ANY  OUTPUT.  By  Frederick  Walker. 
Fully  illustrated. 

Mo.  99.  TRIPLE-EXPANSION  ENGINES  AND  ENGINE 
TRIALS.  By  Prof.  Osborne  Reynolds.  Edited,  with  notes,  etc.,  by 
F.  E.  Idell,  M.  E. 


SCIENCE  SERIES. 


No.  100.  HOW  TO  BECOME  AN  ENGINEER  ;  OR,  THE 
THEORETICAL  AND  PRACTICAL  TRAINING  NECESSARY  IN 
FITTING  FOR  THE  DUTIES  OF  THE  CIVIL  ENGINEER.  The 

Opinions  of  Eminent  Authorities,  and  the  Course  of  Study  in  the 
Technical  Schools.  By  Geo.  W.  Plympton,  Am.  Soc.  C.E. 

No.  101.  THE   SEXTANT  AND   OTHER   REFLECTING 

MATHEMATICAL  INSTRUMENTS.  With  Practical  Suggestions 
and  Wrinkles  on  their  Errors,  Adjustments,  and  Use.  With  thirty- 
three  illustrations.  By  F.  R.  Brainard,  U.S.N. 

No.    102.      THE       GALVANIC      CIRCUIT       INVESTIGATED 

MATHEMATICALLY.  By  Dr.  G.  S.  Ohm,  Berlin,  1827.  Translated 
by  William  Francis.  W.-ii  Preface  and  Notes  by  the  Editor,  Thomas 
D.  Lockwood,  M.I.E.E. 

No.  103.  THE  MICROSCOPICAL  EXAMINATION  OF  POTA- 
BLE WATER.  With  Diagrams,  By  Geo.  W.  Rafter. 

No.  104.     VAN  NOSTRAND'S  TABLE-BOOK  FOR  CIVIL  AND 

MECHANICAL  ENGINEERS.    Compiled  by  Geo.  W.  Plympton,  C.E. 

No.  105.  DETERMINANTS,  AN  INTRODUCTION  TO  THE 

STUDY  OF.     With  examples.     By  Prof.  G.  A.  Miller. 

No.  106.  TRANSMISSION  BY  AIR-POWER.  Illustrated.  By 
Prof.  A.  B.  W.  Kennedy  and  W.  C.  Unwin. 

No.    107.     A  GRAPHICAL   METHOD   FOR   SWING-BRIDGES. 

A  Rational  and  Easy  Graphical  Analysis  of  the  Stresses  in  Ordinary 
Swing- Bridges.  With  an  Introduction  on  the  General  Theory  of  Graphi- 
cal Statics.  4  Plates.  By  Benjamin  F.  LaRue,  C.E. 

No.    108.     A    FRENCH    METHOD    FOR    OBTAINING   SLIDE- 

VALVE  DIAGRAMS.  8  Folding  Plates.  By  Lloyd  Bankson,  B.S., 
Assist.  Naval  Constructor,  U.S.N. 

No.  109.  THE  MEASUREMENT  OF  ELECTRIC  CURRENTS. 

ELECTRICAL  MEASURING  INSTRUMENTS.  By  Jas.  Swinburne.  METERS 
FOR  ELECTRICAL  ENERGY.  By  C.  H.  Wordingham.  Edited  by 
T.  Commerford  Martin.  Illustrated. 

No.  no.  TRANSITION  CURVES.  A  Field  Book  for  Engineers, 
containing  Rules  and  Tables  for  laying  out  Transition  Curves.  By 
Walter  G.  Fox. 

No.  in.     GAS-LIGHTING  AND  GAS-FITTING,  including  Specifica- 
tions and  Rules  for  Gas  Piping,   Notes  on  the  Advantages  of  Gas  for 
Cooking  and   Heating,  and  useful  Hints  to  Gas  Consumers.     Second 
.  edition,  rewritten  and  enlarged.     By  Wm.  Paul  Gerhard. 

No.  112.  A  PRIMER  ON  THE  CALCULUS.  By  E.  Sherman 
Gould,  C.E. 

No.  113.     PHYSICAL   PROBLEMS   AND    THEIR   SOLUTION. 

By  A.  Bourgougnon,  formerly  Assistant  at  Bellevue  Hospital. 

No.  114.     MANUAL  OF  THE  SLIDE  RULE.     By  F.  A.  Halsey  of 

the  American  Machinist.    Second  edition,  revised. 


SCIENCE    SERIES. 


No.   115.     TRAVERSE  TABLES,  showing  the  difference  of  Latitude 
and  Departure  for  distances  between  i  and  100  and  for  Angles  to 

guarter  Degrees  between  i  degree  and  90  degrees.     (Reprinted  from 
:ribner's  Pocket  Table  Book.) 

No.  116.     WORM    AND     SPIRAL     GEARING.       Reprinted    from 
"American  Machinist."     By  F.  A.  Halsey. 


SCIENTIFIC  PUBLICATIONS. 


Catalogue  of  Weale's  Rudimentary 

Scientific  Series. 


®~  "WEALE'S  SEKIES  includes  Text-Books  on  almost  every  branch  of 
Science  and  Industry,  comprising  such  subjects  as  Architecture  and  Building, 
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4.  Mineralogy,  by  Ramsay.    3d  edition,  enlarged 1.40 

6.  Mechanics,  byTomlinson 60 

7.  Electricity,  by  Harris 

7*.  Galvanism  and  Electricity,  by  Harris 

8.  Rudimentary  Magnetism,  by  Harris  and  Noad 

11.  Electric  Telegraph,  History,  by  Sabine 

12.  Pneumatics,  Acoustics,  &c.,  by  Chas.  Tomlinson,  F.R.S.  4th  Edition, 

enlarged 60 

16.  Architecture,  Orders,  by  Leeds 60 

17.  Architecture,  Styles,  by  Bury : .80 

16.  17,  bound  together 1.40 

18.  Architecture.  Design,  by  Garbett 1.00 

16.  17,  and  18,  in  one  vol.  half-bound 2.40 

20.  Perspective,  by  Pyne 80 

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25,  Masonry  and  Stone  Cutting,  by  Dobson 1.00 

31.  Weil-Sinking.     By  Swindell  and  Burnell 80 

32.  Mathematical  Instruments,  by   Heather.     New  Edition,    enlarged  by 

A.  T.  WAUOSLET 80 


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33.  Cranes  and  Machinery,  by  Glynn $0.60 

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35.  Blasting  and  Quarrying,  by  Burgoyne 60 

36.  Dictionary  of  Terms  in  Architecture,   &c.,  by  John  Weale.     Enlarged 

by  Robert  Hunt,  F.K.S 2.00 

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60.  Law  of  Contracts,  by  Gibbons 

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53*  Ships,  Construction  of,  by  Sommerf eldt 60 

53**.  Plates  to  ditto,  4to 3.00 

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64*.  Iron  Ship  Building,  by  Grantham 

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69.  Steam  Boilers,  by  Armstrong 60 

60.  Land  and  Engineering  Surveying,  by  Baker 80 

61*  Ready  Reckoner  for  Land,  by  Annan 80 

67.  Clocks  and  Watches,  and  Bells,  by  Sir  E.  Beckett.        7th  Edition,  re- 
vised and  enlarged .' 1.80 

69.  Music,  by  Spencer 1.00 

71.  Pianoforte  Instruction,  by  Spencer 60 

69  &  71.  Music  and  the  Pianoforte,  by  Spencer.     In  1  vol.  half -bound 

72.  Recent  and  Fossil  Shells,  by  Woodward 

76.  Geometry,  Descriptive,  by  Heather 80 

80.  Marine  Engines,  by  Murray.     8th  Edition,  with  Additions  by  G.  Car- 

lisle,  C.E 1.80 

80*  Embanking  Lands  from  the  Sea,  by  Wiggins 

81.  Water  Works,  by  Hughes 1.60 

83**.  Locks,   Construction  of 1.00 

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83.  Book-keeping,  Haddon 60 

84.  Arithmetic,  by  Young 60 

84*.  Key  to  ditto 60 

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97.  Statics  and  Dynamics,  by  Baker 60 

98.  Mechanism  and  Machines,  by  Baker  and  Nasmyth 1.00 

99.  Navigation  and  Nautical  Astronomy,  by  Young 1.00 

101.  Differential  Calculus,  by  Woolhouse 60 

102.  Integral  Calculus,  by  Cox 60 

106.  Ships'  Anchors,   by  Cotsell 

111.  Arches,  Piers  and  Buttresses,  by  Bland 60 

112.  Domestic  Medicines,  by  Gooding 80 

112*.  The  Management  of  Health,  by  Baird 40 

113.  On  the  Use  of  Field  Artillery,  by  H.  H.  Maxwell 

113.*  Memoir  on  Swords,  by  Col.  Marey 

116.  Acoustics  of  Public  Buildings,  by  Smith 60 

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118.  Civil  Engineering  in  North  America,  by  Stevenson 

127.  Architectural  Modeling,  by  Eichardson 60 

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128,  130,  in  1  vol.  half-bound 2.40 

131.  Miller's,   Corn  Merchant's    and  Farmer's  Beady  Reckoner.     Kevised 

by  Hutton 80 

132.  Dwelling  Houses,  Erection  of,  by  Brooks 1.00 

135.  Electro-metallurgy,  Watt 1.40 

136.  Arithmetic,  by  Haddon 60 

137.  Key  to  ditto 

138.  Telegraph,  Handbook  of,  by  Bond 

139.  Steam  Engins,  Theory  of,  by  Baker 60 

140.  Farming — Soils,  Manures  and  Crops,  by  Burn .80 

141.  Ditto        Outlines— Farming  Economy,  by  Burn 1.20 

142.  Ditto        Cattle,  Sheep  and  Horses,  by  Burn 1.00 

143.  Experimental  Essays,  by  C.  Towlinson 

145.  Farming,  Dairy,  Pigs,  and  Poultry,  by  Burn 80 

146.  Ditto        Sewage,  Irrigation,  &c.,  by  Burn 1.00 

140  to  146.  The5vols.  in  1,  half-bound 4.80 

147.  The  Stepping  Stone  to  Arithmetic,  by  A.  Annan 

148.  Key  to  the  same 


D.  VAX  NOSTRAND  COMPANY'S 


No.  PBICK. 

149.  Sails  and  Sailmaking,  by  Kipping $1.00 

150.  Logic,   by  Emmens 60 

151.  Handy  Book  on  the  Law  of  Friendly,  Industrial  and  Provident  Build- 

ing and  Loan  Societies,  by  A.  White 

153.  Locke  on  the  Understanding,  by  Emmens 60 

154.  General  Hints  to  Emigrants 

155.  Engineer's  Guide  to  the  Navies 

156.  Quantities  and  Measurements,  by  Beaton 60 

157.  Emigrant's  Guide  to  Natal,  by  Dr.  Mann 

158.  Slide  Eule  and  How  to  Use  it,  by  Hoare 1.00 

162.  Brass  Founder's  Manual,  by  W.  Graham 80 

163.  Law  of  Patents  for  Invention,  by  F.  W.  Campin 

164.  Modern  Workshop  Practice,    by  J.  G.  Winton.     Fourth  Edition,  re-- 

vised and  enlarged 1.40 

165.  Iron  and  Heat,  by  Armour 1.00 

166.  Power  in  Motion,  by  Armour 80 

167.  Iron  Bridges,  Girders,  <fcc.,  by  Campin 

168.  Drawing  and  Measuring  Instruments,  by  Heather 63 

169.  Optical  Instruments,  by  Heather 60 

170.  Surveying  arid  Astronomical  Instruments,  by  Heather 60 

168,  169,  170.  The  three  parts  as  above  in  1  vol 1.80 

V  The  above  form  an  enlargement  of  the  original  work,   "  Mathematiccl 

Instruments  "  (No.  32). 
171     Engineering  Drawing,  by  John  Maxton 1.40 

172.  Mining  Tools,  by  William  Morgans 1.00 

172*.  Plates  to  ditto,  235  Engravings,  4to 1.80 

173.  Physical  Geology,  by  Portlock  and  Tate 80 

174.  Historical  Geology,  by  Ralph  Tate,  F.  G.  S 1.00 

173.  174.  Geology,  Portlock  and  Tate,  1  vol 1.80 

175.  Builder's  and  Contractor's  Price  Book 

176.  The  Metallurgy  of  Iron,  by  H.  Bauerman 2.00 

177.  Culture  of  Fruit  Trees,  by  Du  Breuil 1.40 

178.  Practical  Plane  Geometry,  by  J.  F.  Heather 80 

180.  Coal  and  Coal  Mining,  by  W.  W.  Smyth 1.40 

181.  Painting  (Fine  Art),  by  Gullick  and  Timbs 2.00 

182.  Carpentry  and  Joinery,  by  Tredgold  and  Tarn 1.40 

182*.  Atlas  of  35  plates  to  the  above .....  2.40 

183.  Animal  Physics,  by  Dr.  Lardner.     Parti 1.60 

184.  Ditto.     Partn 1.20 

183,184.  Ditto.     In  1  VoL     Cloth  boards 3.00 

185.  The  Complete  Measurer,  by  Richard  Horton 1.60 

186.  Grammar  of  Coloring,  by  Field,  Enlarged  by  Ellis  A.  Davidson,  with 

colored  plates 1.20 


SCIENTIFIC  PUBLICATIONS. 


No.  PBICE. 

187.  Hints  to  Young    Architects,   by  G.   Wightwick,  Enlarged  by  G.  H. 

Guillaume $1.40 

188.  House  Painting,  &c.,  by  Ellis  A.  Davidson 2.00 

189.  Practical  Bricklaying,  by  Adam  Hammond .60 

190.  Steam  and  the  Steam  Engine,  by  D.  K.  Clark 1.40 

191.  Plumbing,    House    Drainage    and    Ventilation,   by  W.    P.   Buchan. 

Fifth  Edition,  Enlarged 1.40 

192.  Timber  Importers' and  Builders' Guide,  by  Grandy 80 

.20 
.40 

194,  112.  112*.  House  Book  (The).     Three  vols.  in  one,  half -bound 40 

.60 


193.  Field  Fortification,  by  Major  W.  W.  Knollys. 

194.  House  Manager,  by  an  Old  Housekeeper 


196.  Compound  Interest  and  Annuities,  by  F.  Thoman 

197.  Koads  and  Streets,  by  Law  and  Clark 

198.  The  Sheep,  by  W.  C.  Spooner 

199.  The  Compendius  Calculator,  by  D.  O'Gorman,  revised  by  C.  Norris.... 


).  Fuel,  by  C.  W.  Williams  and  D.  K.  Clark. 


201.  Kitchen  Gardening  made  Easy,  by  Glenny 

202.  Locomotive  Engines,  by  Dempsey,  with  additions  by  D.  K.  Clark 

203.  Sanitary  Work,  by  Charles  Slagg '. 

204.  Mathematical  and  Nautical  Tables,   with  Treatise  on  Logarithms,  by 


Law  and  Young. 


204*.  Logarithms,  Treatise  on,  with  Tables,  by  Law,  from  the  above 


.40 

00 
.40 


.20 

.00 
.20 
204&55.  Practical  Navigation,  in  1  voL,  half-bound 2.80 

205.  Letter  Painting  Made  Easy,  by  J.  G.  Badenoch 60 

206.  A  Book  on  Building,  by  Sir  Edmund  Beckett 1.80 

207.  Farm  Management,  by  R.  Scott  Burn 1.00 

208.  Landed  Estates  Management,  by  R.  Scott  Burn 1.00 

207,  208.  Farm  and  Landed  Estates  Management,  by  R.  Scott  Burn,  in  1 

vol.,  half-bound 2.40 

209.  The  Tree  Planter  and  Plant  Propagator :  A  Practical  Manual,  by  Sam- 

uel Wood 80 

210.  The  Tree  Pruner,  by  Samuel  Wood 60 

209,  210.  The  Tree  Planter,  Propagator,  and  Pruner,  by  Samuel  Wood.    In 

1vol.,  half-bound 1.40 

211.  The  Boilermaker's  Assistant,  by  Courtney 80 

212.  The  Construction  of  Gasworks,  by  S.  Hughes.     Seventh  Edition  by 

William  Richards 2.20 

213.  Pioneer  Engineering,  by  Edward  Dobson,   C.  E 1.80 

214.  Slate  and  Slate  Quarrying,  by  D.  C.  Davies 1.20 

215.  The  Goldsmith's  Handbook,  by  G.  E.  Gee 1.20 

216.  Materials  and  Construction,  by  F.  Campin 1.20 

217.  Sewing  Machinery,  by  J.  W.  Urquhart,  C.  E 80 

218.  Hay  and  Straw  Measurer,  by  John  Steele 80 


D.  VAN  NOSTBAND  COMPANY'S 


No.  PEICE. 

219.  Civil  Engineering,  by  Law  and  Burnell,  with  Recent  Practice,  by  D. 

K.  Clarke,  M.  I.  C.  E $2.60 

221.  Measures,  Weights,  and  Moneys  of  All  Nations,  by  W.  S.  B.  Woolhouse. 

New  Edition 1.00 

222.  Suburban  Farming,  by  Prof .  Donaldson 

223.  Mechanical  Engineering,  by  F.  Camp  in,  C.  E 1.00 

224.  Coach  Building,  by  Jas.  W.  Burgess 1.00 

225.  The  Silversmith's  Handbook,  by  G.  E.  Gee 1.20 

215,  225.  The  Goldsmith's  and  Silversmith's  Complete  Handbook,  by  Gee. 

half-bound 2.80 

226.  The  Joints  used  by  Builders,  by  J.  W.   Christy 1.20 

227.  Mathematics  as  applied  to  the  Constructive  Arts,  by  F.  Campin,  C.  E.  1.20 

228.  The  Construction  of  Roofs,  by  E.  W.  Tarn 60 

229.  Elementary  Decoration,  by  J.  W.  Facey 80 

230.  Hand  Railing  by  Geo.  Ceilings 1.00 

231.  Grafting  and  Buding,  by  C.  Baltet 1.00 

232.  Cottage  Gardening,  by  E.  Hobday 60 

233.  Garden  Receipts.     Edited  by  C.  W.  Quin 60 

234.  Market  and  Kitchen  Gardening,  by  C.  W.  Shaw 1.20 

235.  Practical  Organ-Building,  by  Dickson 1.00 

236.  Details  of  Machinery,  by  F.  Campin,  C.  E 1.20 

237.  The  Smithy  and  Forge,  by  Crane.     2d  Edition 1.00 

238.  Sheet  Metalworkers'  Guide,  by  Crane 60 

239.  Draining  and  Embanking,  by  Prof .  Scott 60 

240.  Irrigation  and  Water  Supply,  by  Prof.  Scott 60 

241.  Farm  Roads,  Fences  and  Gates,  by  Prof.  Scott .60 

242.  Farm  Buildings,  by  Prof.  Scott 80 

243.  Barn  Implements  and  Machines,  by  Prof.  Scctt 80 

244.  Field  Implements  and  Machines,  by  Pros.  Scott 80 

245.  Agricultural  Surveying,  by  Prof .  Scoit 60 

239  to  245.  The  7  vols.  in  1,  half -bound 4.80 

246.  Dictionary  of  Painters,  by  P.  Datyl 1.00 

247.  Building  Estates,  by  Fowler  Maitland 80 

248.  Portland  Cement  for  Users,  by  Faija 80 

249.  The  Hall-Marking  of  Jewelry,  by  Gee 1.20 

250.  Meat  Production,  by  John  Ewart l.OC 

251.  Steam  and  Machinery  Management,  by  M.  Powis  Bale,  C.  E 1.00 

252.  Brickwork,  a  Practical  Treatise,  by  F.  Walker.     2nd  Edition,  revised..     .60 
23,  189  &  252.  The  Practical  Brick  and  Tile  Book,  in  1  volume,  half -bound. 

253.  The  Timber  Merchant's  Freight  Book,  by  W.  Richardson  and  M.  P.  Bale, 

254.  The  Boilermaker's  Ready  Reckoner,  by  J.  Courtney,  revised  by  D. 

K.  Clark 1.60 

251  and  211  in  one  volume,  half  bound. ...  ...  2.80 


SCIENTIFIC  PUBLICATIONS. 


No.  PBICE. 

256.  Stationary  Engine  Driving,  by  Michael  Reynolds $1.40 

257.  Practical  House  Decoration,  by  Facey 1.00 

229,  257.  House  Decoration,  by  Facey,  in  1  volume,  half-bound 2.00 

258.  Circular  Work  in  Carpentry,  by  Collings 1.00 

259.  Gas-Fitting,  by  John  Black 1.00 

260.  Iron  Bridges  of  Moderate  Span,  by  Hamilton  W.  Pendred 80 

261.  Shoring,  by  Geo.  H.  Blagrove 60 

262.  Boot  and  ShoemaMng,  by  J.  B.  Leno .80 

263.  Mechanical  Dentistry,  by  C.  Hunter 1.20 

264  Miningand   Quarrying,  by  J.  H.  Collins 60 

265.  Practical  Brick  Cutting  and  Setting,  by  Adam  Hammond. 60 

23,  189,  265  in  one  volume,  half  bound 2.40 

267.  The  Science  of  Building,  by  E.  W.  Tarn 1.40 

268.  The  Drainage  of  Lands,  Towns  and  Buildings,  by  G.  D.  Dempsey. 

Revised,  with  additions,  by  D.  K.  Clark.     2d  ed 1.80 

269.  Light;  an  Introduction  to  the  Science  of  Optics,  by  E.  W.  Tarn 60 

270.  Wood  Engraving,  by  W.  N.  Brown 60 

271.  Ventilation,  by  W.  P.  Buchan 1-40 

272.  Roof  Carpentry,  by  George  Collings 80 

273.  The  Practical  Plasterer,  by  W.  Kemp 8C 

274.  Elementary  Marine  Engineering,  by  J.  S.  Brewer 60 

275.  Laundry  Management 80 

276.  Cement,  Pastes,  Glues  and  Gums,  by  H.  C.  Standage 80 

277.  Fuels  ;  Their  Analysis  and  Valuation,  by  H.  J.  Phillips 80 

278.  Model  Locomotive  Engineer,  Fireman,  &c.,  by  M.  Reynolds 1.40 

279.  Constructional  Iron  and  Steel  Work,  by  F.  .Campin 1. 40 

280.  Iron  and  Steel  Bridges  and  Viaducts,  by  F.  Campin 1.40 

281.  French  Polishing  and  Enamelling,  by  R.  Bitmead 60 

282.  Electric  Lighting,  by  A.  A.  C.  Swinton 60 


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